
614 So.2d 517 (1992)
ROYAL CARIBBEAN CORPORATION, as successor in interest to Poseidon Services, Ltd., S.A., and Sun Viking, Inc., as successor in interest to P.R. Sun Viking, Appellants/Cross-Appellees,
v.
Jerry MODESTO, Appellee/Cross-Appellant.
Nos. 90-523, 90-757.
District Court of Appeal of Florida, Third District.
December 8, 1992.
Rehearing Denied April 6, 1993.
*518 Fowler, White, Burnett, Hurley, Banick & Strickroot, Mark R. Houck and John W. Keller, III, Miami, for appellants/cross-appellees.
Rivkind & Pedraza and Brett Rivkind, Miami, for appellee/cross-appellant.
Before JORGENSON, GERSTEN and GODERICH, JJ.
JORGENSON, Judge.
Royal Caribbean and Sun Viking appeal from a final judgment following a jury trial. We affirm the final judgment and reverse and remand on the issue of plaintiff's entitlement to attorney's fees.
Jerry Modesto sued Royal Caribbean and Sun Viking under the Jones Act, 46 U.S.C.A. § 688 (1982), and general maritime law for personal injuries he sustained aboard ship. Before trial, the plaintiff served a demand for judgment pursuant to section 768.79, Florida Statutes (1989), in the amount of $225,000. Defendants did not respond, and the court ordered the parties to mediation. Although the mediation was unsuccessful and the results of the proceeding were therefore never reduced to a written agreement, defendants moved to enforce an oral settlement agreement which they alleged was reached during the mediation proceedings, and subpoenaed the mediator to testify at a hearing on the motion. The mediator moved to quash the subpoena, invoking the privilege codified in section 44.302, Florida Statutes (1987), which provides that "[e]ach party involved in the mediation proceeding has a privilege to refuse to disclose, and to prevent any person present at the proceeding from disclosing, communications made during such proceeding whether or not the dispute was successfully resolved." The trial court granted the motion to quash and did not permit the defendants to present any testimony regarding the mediation proceedings. The cause proceeded to trial and resulted in a verdict and judgment for the plaintiff in the amount of $499,000 plus costs. Plaintiff's counsel moved for fees pursuant to section 768.79, Florida Statutes (1989). The trial court denied the motion and declared section 768.79 an unconstitutional infringement upon the rulemaking authority of the Florida Supreme Court. Defendants appeal, arguing that the trial court erred in failing to conduct an evidentiary hearing on their motion to enforce the settlement agreement and in applying to a federal maritime action the privilege afforded mediators by Florida statute. Plaintiff cross-appeals the denial of attorney's fees.
Principles of substantive federal law apply to Jones Act cases brought in state court, and the enforceability and validity of settlement agreements reached in those cases is determined by federal law  at least where the substantive rights and liabilities of the parties derive from federal law. Borne v. A & P Boat Rentals, 780 F.2d 1254, 1256 (5th Cir.1986); Hallman v. Carnival Cruise Lines, Inc., 459 So.2d 378 (Fla. 3d DCA 1984).[1] However, it is not, and cannot be, the rule of law that federal law also governs all procedural and evidentiary issues that arise and that federal maritime *519 law supersedes Florida's Mediation Act.
"The States ... have great latitude to establish the structure and jurisdiction of their own courts. In addition, States may apply their own neutral procedural rules to federal claims, unless those rules are preempted by federal law. These principles are fundamental to a system of federalism in which the States share responsibility for the application and enforcement of federal law." Howlett v. Rose, 496 U.S. 356, 372; 110 S.Ct. 2430, 2441; 110 L.Ed.2d 332, 351 (1990) (citations omitted).[2]See also Steelmet, Inc. v. Caribe Towing Corp., 779 F.2d 1485 (11th Cir.1986) (state may create direct action against maritime insurer where such action does not conflict with any feature of substantive admiralty law or any remedy peculiar to admiralty jurisdiction). A Jones Act claim brought in state court is governed by federal substantive law; however, federal law does not preempt the procedural scheme designed by the Florida legislature to mediate claims as an alternative to judicial action.
Florida's evidence code "recognizes privileges when the legislature judges the protection of an interest or relationship is sufficiently important to society to justify the sacrifice of facts which might be needed for the administration of justice." Ehrhardt, Florida Evidence § 501.1 (1992 Ed.). The privilege afforded to parties involved in mediation proceedings, and asserted by the mediator in the trial court, was codified by the Florida legislature in section 44.302(2), Florida Statutes (1989). The privilege contravenes no federal rule of substance or procedure and plays a central role in Florida's mediation scheme by preserving the neutrality of the mediator. Cf. Hudson v. Hudson, 600 So.2d 7, 8-9 (Fla. 4th DCA 1992) (holding that the "well was poisoned" by the admission, during trial, of an agreement allegedly reached during a mediation proceeding and ordering a new trial, because "the injection of the so-called agreement prepared by [a party] and `certified' by the mediator ... violates the spirit and letter of the mediation statute."), and Fabber v. Wessel, 604 So.2d 533 (Fla. 4th DCA 1992) (same). Florida's supreme court recognized that confidentiality of the proceedings is crucial to mediation by mandating that "[i]f the parties do not reach an agreement as to any matter as a result of mediation, the mediator shall report the lack of an agreement to the court without comment or recommendation," and by further requiring that "[i]f an agreement is reached, it shall be reduced to writing." Fla.R.Civ.P. 1.730 (emphasis added). No such writing resulted from the failed mediation in this case. Accordingly, the trial court properly quashed the subpoena directed at the mediator and declined to take any testimony regarding the mediation proceeding.
Preserving Florida's scheme of mediation does not affect the rule that the validity of settlement agreements in Jones Act cases brought in state court is to be determined by federal substantive law or the principle that oral settlement agreements arrived at through means other than mediation may be recognized in such cases. Cf. Kossick v. United Fruit Co., 365 U.S. 731, 734; 81 S.Ct. 886, 889; 6 L.Ed.2d 56, 60 (1961) (New York statute of frauds inapplicable to dispute arising out of oral contract concerning seaman's maintenance and cure; Court recognized that "it is an established rule of ancient respectability that oral contracts are generally regarded as valid by maritime law."). However, probes into the inner workings of a mediation proceeding that was conducted pursuant to Florida statute must remain governed by Florida law.
*520 This court has previously applied Florida's procedural and evidentiary rules to actions for damages brought pursuant to the Jones Act. See, e.g., Canales v. Compania de Vapores Realma, 564 So.2d 1212 (Fla. 3d DCA 1990) (trial court committed reversible error in Jones Act case in refusing to admit deposition of designated corporate representative into evidence and in limiting its use to impeachment purposes only, contrary to Florida Rule of Civil Procedure 1.330(a)(3)); Carnival Cruise Lines v. Rodriguez, 505 So.2d 550 (Fla. 3d DCA 1987) (trial court violated Florida rule of evidence in admitting portion of ship's medical log in Jones Act case). Therefore, application of the mediation privilege was not error, and we accordingly affirm the judgment under review.
On plaintiff's cross-appeal of the denial of attorney's fees, we reverse. We do not address the constitutionality of section 768.79, Florida Statutes (1989), as the Florida Supreme Court, when given the opportunity to declare section 768.79 an unconstitutional infringement on its rulemaking authority, expressly declined to do so. The Florida Bar Re: Amendment to Rules of Civil Procedure Rule 1.442 (Offer of Judgment), 550 So.2d 442 (Fla. 1989). Instead, the court amended Fla.R.Civ.P. 1.442 and held that "[t]o the extent that procedural aspects of new rule 1.442 are inconsistent with sections 768.79 and 45.061, the rule shall supersede the statutes." Amendment to Rules of Civil Procedure Rule 1.442, 550 So.2d at 443.
Moreover, in accordance with the principles of law announced in this case, we find no conflict between Florida's rules of law regarding offers of judgment and federal maritime law.[3] In federal admiralty actions, an award of attorney's fees as a component of maintenance and cure is traditionally within the equitable jurisdiction of the courts. Vaughan v. Atkinson, 369 U.S. 527, 82 S.Ct. 997, 8 L.Ed.2d 88 (1962). Awards of attorney's fees made pursuant to Florida law regarding offers of judgment are intended to deter unnecessary litigation and encourage the timely settlement of claims, just as Florida laws regarding mediation are intended to provide an efficient alternative to litigation of claims. Because Florida's rules relating to offers of judgment are an integral part of this state's management of its courts' proceedings and do not conflict with federal admiralty law, we reverse the order denying attorney's fees and remand to the trial court for further proceedings.
Affirmed in part; reversed in part; remanded.
NOTES
[1]  Moreover, in this case the parties stipulated that federal maritime law applies.
[2]  The Federal Rules of Evidence even provide that "[i]n civil actions and proceedings, with respect to an element of a claim or defense as to which State law supplies the rule of decision, the privilege of a witness ... shall be determined in accordance with State law." Fed. R.Evid. 501. See also Gulliver's Periodicals, Ltd. v. Chas. Levy Circulating Co., 455 F. Supp. 1197, 1200 (N.D.Ill. 1978) ("In federal question cases and cases where federal law governs, the clear weight of authority supports reference to federal law on the existence and scope of a privilege. However, where ... there is no controlling federal statute on the asserted privilege, the district court for its guidance may consider existing state law concerning the privilege.")
[3]  See also Fed.R.Civ.P. 68 (providing for costs when offer of judgment not accepted), and Marek v. Chesny, 473 U.S. 1, 105 S.Ct. 3012, 87 L.Ed.2d 1 (1985) (holding that term "costs" includes attorney's fees when underlying statute giving rise to cause of action defines costs to include attorney's fees).
