
573 F.3d 578 (2009)
DONALDSON COMPANY, INC., Plaintiff-Appellee,
v.
BURROUGHS DIESEL, INC., Defendant-Appellant.
No. 08-2705.
United States Court of Appeals, Eighth Circuit.
Submitted: March 13, 2009.
Filed: July 20, 2009.
*580 Michael Gross, argued, Joseph F. Yeckel, on the brief, St. Louis, MO, for appellant.
Roger James Magnuson, argued, Minneapolis, MN, Reed Waller Sugg, Bryan Patrick Cavanaugh, St. Louis, MO, Richard M. Dye, Robert A. Miller, on the brief, Jackson, MS, for appellee.
Before SMITH, GRUENDER, and BENTON, Circuit Judges.
BENTON, Circuit Judge.
Donaldson Company, Inc., a nonsignatory, seeks to compel arbitration against Burroughs Diesel, Inc., a signatory to an agreement with an arbitration clause. The district court ordered arbitration. Burroughs appeals. Jurisdiction being proper under 28 U.S.C. § 1291, this court reverses.

I.
In 1999, Burroughs signed a Dealer Full Service Agreement with Western Star Truck Sales, Inc. Western Star manufactured trucks that it sold to Burroughs for resale. A third party, Donaldson, supplied two parts of the air intake system in the trucks. The Dealer Agreement did not *581 mention Donaldson. It contained an arbitration provision that
any controversy or claim arising out of or in connection with this Agreement, its construction, interpretation, effect, performance, nonperformance, termination, or consequences thereof, or any transaction contemplated hereby, however characterized as a matter of law (whether in contract, tort or otherwise), ... shall be settled by arbitration in St. Louis County, Missouri....
Dealer Agreement ¶ 31. The Agreement provided that it "shall be governed by and construed in accordance with the laws of the state in which Dealer's principal place of business, as designated in Paragraph 6 hereof, is located, and such laws shall be applied and control any arbitration conducted pursuant to Paragraph 31 hereof." Id. ¶ 34.[1]
The engines failed in several trucks purchased from Burroughs. In November 2001, the buyers sued Donaldson, "Western Star Trucks," and Burroughs in Mississippi state court. In February 2002, Burroughs cross-claimed against Donaldson and Western Star. The cross-claim, referring to Donaldson and Western Star collectively as "Cross-Defendants," did not distinguish between them in terms of the misconduct alleged. Western Star answered the cross-claim, raising arbitration as an affirmative defense, and serving a copy on Donaldson.
Two days later, Western Star sued, in the U.S. District Court for the Eastern District of Missouri, to compel arbitration. Neither Burroughs nor Western Star notified Donaldson of the arbitration proceedings in Missouri.
In Mississippi, Donaldson answered the cross-claims, conditionally raising an arbitration defense: "If there is an arbitration agreement between Western Star Trucks and Burroughs, then the cross-claim is barred by that agreement and the cross claim should be dismissed and all issues should be resolved by arbitration." Donaldson raised other affirmative defenses, including "lack of privity" and the lack of a "legal, contractual, or other relationship" between Donaldson and Burroughs.
In December 2002, the Missouri district court granted Western Star's motion to compel arbitration, relying on the arbitration clause in the Dealer Agreement. See Western Star Truck Sales, Inc. v. Burroughs Diesel, Inc., No. 4:02-cv-457, slip op. at 9 (E.D.Mo. Dec. 2, 2002). Burroughs then dismissed its Mississippi cross-claim against Western Star.
In August 2007, Burroughs moved to schedule trial on its cross-claim against Donaldson in Mississippi. Soon thereafter, Donaldson alleges, it first learned of the Missouri arbitration order. In October 2007, Donaldson moved to compel Burroughs to arbitrate in the Missouri district court, citing that court's 2002 arbitration order in the Western Star-Burroughs case.
In Missouri, Donaldson argued that, although it was not a party to the Dealer Agreement, arbitration was required because: 1) Burroughs's claim was premised on and presumed the existence of the Agreement; and 2) Burroughs previously alleged that Western Star and Donaldson acted in concert. Burroughs responded by moving for summary judgment, which was denied. The district court granted Donaldson's motion to compel arbitration, enjoining Burroughs from proceeding in Mississippi court.[2]


*582 II.
This court reviews "de novo a district court's grant of a motion to compel arbitration." 3M Co. v. Amtex Sec., Inc., 542 F.3d 1193, 1198 (8th Cir.2008). "A court must grant a motion to compel arbitration if a valid arbitration clause exists which encompasses the dispute between the parties." Id. The parties agree that paragraph 31 of the Agreement is a valid arbitration clause. They dispute whether Donaldson's claim is within its scope. Donaldson was not a party to the Agreement, and must rely on the doctrine of equitable estoppel in the arbitration context. See, e.g., Dominium Austin Partners, LLC v. Emerson, 248 F.3d 720, 728 (8th Cir.2001).

A.
Burroughs argues that Mississippi law, not federal law, should apply based on the choice-of-law provision in the Agreement. "This court reviews a district court's choice of law determination de novo." Am. Home Assurance Co. v. L & L Marine Serv., Inc., 153 F.3d 616, 618 (8th Cir.1998). "When deciding whether the parties agreed to arbitrate a certain matter..., courts generally ... should apply ordinary state-law principles that govern the formation of contracts." Hudson v. ConAgra Poultry Co., 484 F.3d 496, 500 (8th Cir.2007), quoting First Options of Chicago, Inc. v. Kaplan, 514 U.S. 938, 944, 115 S.Ct. 1920, 131 L.Ed.2d 985 (1995). Thus, state law determines questions "concerning the validity, revocability, or enforceability of contracts generally." Perry v. Thomas, 482 U.S. 483, 493 n. 9, 107 S.Ct. 2520, 96 L.Ed.2d 426 (1987).
The Federal Arbitration Act "create[s] a body of federal substantive law of arbitrability, applicable to any arbitration agreement within the coverage of the Act." Moses H. Cone Mem'l Hosp. v. Mercury Constr. Corp., 460 U.S. 1, 24, 103 S.Ct. 927, 74 L.Ed.2d 765 (1983). In Finnie v. H & R Block Financial Advisors, Inc., this court considered whether an arbitration provision applied to an employment discrimination complaint by an employee against her former employer and supervisor. 307 Fed.Appx. 19 (8th Cir.2009) (per curiam) (unpublished). The employer was a signatory to the employment document with the arbitration clause, but the supervisor was not. Applying Missouri law instead of federal law, the district court concluded the arbitration provision was not enforceable by the nonsignatory supervisor. This court reversed, "conclud[ing] that the district court erred in applying Missouri law to determine whether [the nonsignatory supervisor] could enforce the arbitration agreement. Id. at 21, citing Moses H. Cone, 460 U.S. at 24, 103 S.Ct. 927. See UHC Mgmt. Co., Inc. v. Computer Scis. Corp., 148 F.3d 992, 996-97 (8th Cir.1998) (applying federal law); Dominium Austin Partners, 248 F.3d at 728 (same); Hudson, 484 F.3d at 502-03 (same).
Other circuits also apply the federal substantive law of arbitrability to resolve this issue. See, e.g., Washington Mut. Fin. Group, LLC v. Bailey, 364 F.3d 260, 267 n. 6 (5th Cir.2004); International Paper Co. v. Schwabedissen Maschinen & Anlagen GMBH, 206 F.3d 411, 417-18 (4th Cir. 2000); Grigson v. Creative Artists Agency LLC, 210 F.3d 524, 527 (5th Cir.2000); Thomson-CSF, S.A. v. Am. Arbitration Ass'n, 64 F.3d 773, 778 (2d Cir.1995); Sunkist Soft Drinks, Inc. v. Sunkist Growers, Inc., 10 F.3d 753, 756-58 (11th Cir.1993); Hughes Masonry Co., Inc. v. Greater Clark County Sch. Bldg. Corp., 659 F.2d *583 836, 838-39 (7th Cir.1981). But see Motorola Credit Corp. v. Uzan, 388 F.3d 39, 50-51 (2d Cir.2004) (applying Swiss law between transnational parties); Fleetwood Enters., Inc. v. Gaskamp, 280 F.3d 1069, 1074-75 (5th Cir.2002) (applying Texas law to determine whether a particular nonsignatory was bound by an arbitration agreement).
The issue in this case is whether Donaldson, a nonsignatory, can enforce the arbitration provision in the Agreement. This court concludes that the federal substantive law of arbitrability applies.

B.
"A nonsignatory can enforce an arbitration clause against a signatory to the agreement in several circumstances." CD Partners v. Grizzle, 424 F.3d 795, 798 (8th Cir.2005). "One is when `the relationship between the signatory and nonsignatory defendants is sufficiently close that only by permitting the nonsignatory to invoke arbitration may evisceration of the underlying arbitration agreement between the signatories be avoided.'" Id., quoting MS Dealer Serv. Corp. v. Franklin, 177 F.3d 942, 947 (11th Cir.1999). Another is "when the signatory to a written agreement containing an arbitration clause must rely on the terms of the written agreement in asserting [its] claims against the nonsignatory." Grizzle, 424 F.3d at 798 (internal citations omitted). "When each of a signatory's claims against a nonsignatory makes reference to or presumes the existence of the written agreement, the signatory's claims arise out of and relate directly to the written agreement, and arbitration is appropriate." Id. This second circumstance is derived from the "intertwined claims" doctrine, that a nonsignatory may enforce an arbitration provision where the signatory alleges "substantially interdependent and concerted misconduct" by the nonsignatory and one or more of the signatories. See, e.g., Grigson, 210 F.3d at 527; MS Dealer, 177 F.3d at 947. Donaldson argues that both circumstances apply.

1.
First, Donaldson argues that its relationship is sufficiently close to Burroughs that it is entitled to enforce the arbitration provision. Donaldson cites Ingstad v. Grant Thornton, LLP, which held that a "`close relationship' ... may be found in the structure of the [plaintiff's] complaint." No. 3:05-cv-98, 2006 WL 3751204, at *6 (D.N.D. Dec.19, 2006). Donaldson misreads that case. Ingstad relies on Denney v. BDO Seidman, which applies the intertwined-claims test rather than the sufficiently-close standard:
We have previously indicated that signatories to an arbitration agreement can be compelled to arbitrate their claims with a non-signatory where a careful review of the relationship among the parties, the contracts they signed ..., and the issues that had arisen among them discloses that the issues the nonsignatory is seeking to resolve in arbitration are intertwined with the agreement that the stopped party has signed.
412 F.3d 58, 70 (2d Cir.2005) (internal citations omitted) (emphasis added). Unlike the intertwined-claims test, which looks to the claims asserted, the close-relationship test analyzes the relationship between the signatory and nonsignatory parties "under agency or related principles." MS Dealer, 177 F.3d at 947. Donaldson cannot establish a sufficiently close relationship to BurroughsDonaldson's pleadings stated a "lack of privity between Donaldson and Burroughs," and the lack of any "legal, contractual, or other relationship."


*584 2.
Second, as to the intertwined-claims doctrine, Donaldson argues that Burroughs's cross-claims relied on the Agreement. As a parts supplier for the Western Star trucks sold to Burroughs under the Agreement, Donaldson claims it is entitled to enforce the arbitration provision under Grizzle.
In Grizzle, C.D. Warehouse, Inc. (CDWI) and C.D. Partners signed franchise agreements with identical arbitration clauses. 424 F.3d at 797. C.D. Partners sued CDWI's chief executive officer, chief financial officer, and chief operating officer, charging negligence, negligent misrepresentation, and fraudulent misrepresentation arising out of the franchise agreements. Although the defendant-officers were not parties to the franchise agreements, they moved to compel arbitration. This court ordered arbitration based on the relationship of the parties, and C.D. Partners' allegations:
This case involves an ongoing relationship where signatory CDWI's promises could only be fulfilled by the future conduct of its corporate officers, employees, and agents. The current dispute between signatory C.D. Partners and nonsignator[y officers] arises out of and relates directly to the contractual agreement between the signatories, where the core of the dispute is the conduct of the three nonsignatories in fulfilling signatory CDWI's promises.
Id. at 799.
In this case, Burroughs cross-claimed against Western Star and Donaldson for: negligence, breach of fiduciary duty, breach of good faith and fair dealing, fraudulent misrepresentation, fraudulent concealment, and implied warranty of fitness for a particular purpose. Burroughs's allegations did not refer to the Agreement, and did not arise out of Donaldson's conduct in circumstances similar to the parties in Grizzle. First, the Grizzle court emphasized that the CDWI officers were within the "ambit of the arbitration clause" because the agreement specifically conferred rights upon the "Franchisor's officers, directors, and employees." See id. at 800. The Agreement in the present case does not specifically confer any rights on Donaldson.
Second, the Grizzle court noted that the signatory's duties "could only be fulfilled by the future conduct of its corporate officers, employees, and agents." Id. In equitable estoppel cases, arbitration provisions apply in agency, suretyship, and close affiliation situations. See Sokol Holdings, Inc. v. BMB Munai, Inc., 542 F.3d 354, 358-62 (2d Cir.2008) (listing cases); Finnie, 307 Fed.Appx. at 21 (a nonsignatory may enforce an arbitration provision because he was a supervisor with the signatory-defendant). In this case, there is no such agency, suretyship, or close affiliation relationship. Donaldson has no relationship to Western Star or Burroughs other than supplying parts for the trucks at issue. Donaldson's interpretation of Grizzle would allow any supplier to enforce an arbitration provision if the manufacturer agreed to arbitration. This court declines to extend this interpretation of Grizzle to the present case.
This case is similar to Brantley v. Republic Mortgage Insurance Co., 424 F.3d 392 (4th Cir.2005). There, the plaintiffs bought and financed a home. Their mortgage lender, SouthStar Funding, required them to obtain private mortgage insurance. The plaintiffs obtained it from Republic Mortgage, but later sued Republic for charging excessive premiums. Republic sought to compel arbitration because the "insurance contract is so intertwined with the mortgage and arbitration contracts *585 between the plaintiffs and SouthStar." Id. at 395. The court rejected the argument: "the mere existence of a loan transaction requiring plaintiffs to obtain mortgage insurance cannot be the basis for finding their federal statutory claims, which are wholly unrelated to the underlying mortgage agreement, to be intertwined with that contract." Id. at 396.
In this case, like Brantley, the supply-chain relationship is not sufficient to conclude that Donaldson is intertwined with a party to the Agreement such that it could enforce the arbitration agreement. See also Denney, 412 F.3d at 70 ("The question... [is] whether plaintiffs' claims against the [nonsignatory defendants] are so `intimately founded in' or `intertwined with' the underlying obligations of the [ ] agreements as to allow the non-signatory [party] to compel arbitration."). Donaldson has failed to demonstrate that Burroughs's cross-claim arises out of or relates to the Agreement.
Donaldson also asserts that Burroughs's allegations presume the existence of the Agreement. Burroughs does not allege that the Agreement has been breached. More importantly, Burroughs's cross-claim would have a basis for recovery against Donaldson even if there were no Agreement. Cf. MS Dealer, 177 F.3d at 947-48 (compelling arbitration because "each of [the plaintiff's] fraud and conspiracy claims depends entirely upon her contractual obligation ... for the service contract"); Sunkist, 10 F.3d at 758 ("Although [the signatory] does not rely exclusively on the license agreement to support its claims, each claim presumes the existence of such an agreement."). This court concludes that Burroughs's cross-claim did not presume the existence of the Agreement, or necessarily rely on its terms in asserting its claims.
Donaldson also argues that the cross-claim itself satisfies the intertwined-claims test by alleging "substantially interdependent and concerted misconduct" by Western Star and Donaldson. "[T]he focus of our inquiry should be on the nature of the underlying claims asserted by [the signatory] against [the nonsignatory] to determine whether those claims fall within the scope of the arbitration clause." Sunkist, 10 F.3d at 757-58; accord MS Dealer, 177 F.3d at 947.
The cases applying the concerted-misconduct test establish that the plaintiff must specifically allege coordinated behavior between a signatory and a nonsignatory. In MS Dealer, Franklin, a car buyer, signed a Buyers Order to purchase a car from Jim Burke Motors, Inc. 177 F.3d at 944-47. The Order incorporated by reference a Retail Installment Contract, which obligated the buyer to a service contract through MS Dealer Service Corporation. The Order contained an arbitration clause. When the buyer had problems with the car, she sued Burke and MS Dealer. According to her complaint, Burke and MS Dealer "improperly cooperated, conspired, and otherwise colluded" to charge an excessive amount for the service contract. MS Dealer sought to compel arbitration, which the district court denied because MS Dealer was not a signatory to the Order. The Eleventh Circuit reversed, concluding "that Franklin's claims against Jim Burke and MS Dealer `are based on the same facts and are inherently inseparable.'" Id. at 948. The court emphasized that the buyer "specifically alleges that MS Dealer worked hand-in-hand with Jim Burke and Chrysler Credit Corporation in this alleged fraudulent scheme." Id.
In Denney, the plaintiffs claimed that they were recruited by two accounting firms to participate in a fraudulent tax scheme, Currency Options Bring Reward *586 Alternatives (COBRA). The plaintiffs' "consulting agreements" with the firms contained broad arbitration clauses. The firms, along with Deutsche Bank, advised and executed an illegal plan where plaintiffs manufactured losses from partnerships engaged in foreign currency option transactions. The plaintiffs sued; defendants sought to compel arbitration. The district court held that the consulting agreements were "mutually fraudulent" and unenforceable, and denied a motion to compel arbitration. The Second Circuit reversed and remanded for consideration whether Deutsche Bank, a nonsignatory, could enforce the arbitration provision. The court noted, "[h]aving alleged ... that the Deutsche Bank and BDO defendants acted in concert to defraud plaintiffs ... plaintiffs cannot now escape the consequence of those allegations...." Id. at 70. In particular, the court noted that the complaint alleged that the "Defendants knowingly acted in concert to market and implement the fraudulent and illegal COBRA tax shelter transaction." Id. (emphasis added). See also Ingstad, 2006 WL 3751204, at *5 (following Denney).
In the present case, Burroughs's cross-claim stated that "Cross-Defendants concealed and misrepresented the fact that Western Star Heritage model truck was designed, manufactured and sold with an allegedly defective intake system." The pleading also said that "Cross-Defendants conduct was intentional and/or done with gross negligence." Although Burroughs's cross-claim made common allegations against Western Star and Donaldson, it did not make any allegations suggesting that Western Star and Donaldson "knowingly acted in concert," "improperly cooperated," or "worked hand-in-hand." The concerted-misconduct test requires allegations of "pre-arranged, collusive behavior" demonstrating that the claims are "intimately founded in and intertwined with" the agreement at issue. MS Dealer, 177 F.3d at 948. This court concludes that Burroughs's cross-claim does not rise to the level of "substantially interdependent and concerted misconduct" required by the case law.

III.
The order compelling arbitration is reversed, and the case remanded for further proceedings consistent with this opinion.
NOTES
[1]  Paragraph 6 says that Laurel, Mississippi, is Burroughs's principal place of business.
[2]  In February 2008, the plaintiff-buyers settled with Burroughs, Western Star, and Donaldson, dismissing their claims. The only claim pending in Mississippi is Burroughs's cross-claim against Donaldson.
