
872 S.W.2d 248 (1993)
REYNOLDS, SHANNON, MILLER, BLINN, WHITE & COOK, a Texas Partnership in Dissolution, et al., Appellants,
v.
Donald H. FLANARY, Appellee.
No. 05-93-01505-CV.
Court of Appeals of Texas, Dallas.
December 13, 1993.
Rehearing Denied February 1, 1994.
*249 Bruce K. Watkins, Houston, for appellants.
David Stagner, Sherman, for appellee.
Before LAGARDE, MORRIS and WHITTINGTON, JJ.

OPINION
LAGARDE, Justice.
Appellants appeal an August 27, 1993 temporary injunction entered by the 336th District Court of Grayson County. The temporary injunction prohibits the law firm of Reynolds, Shannon, Miller, Blinn, White & Cook, a partnership in dissolution, from appearing in any way in a suit that it filed in Harris County. The injunction also mandates Reynolds, Shannon to withdraw all deposition notices, hearing notices, and trial settings in the Harris County suit.[1] Appellants assert that the trial court abused its discretion by doing so. We agree. Accordingly, we dissolve the trial court's August 27, 1993 temporary injunction.

PROCEDURAL BACKGROUND
On April 24, 1991, Reynolds, Shannon filed suit against Donald H. Flanary in County Court at Law Number 4 in Harris County, *250 Texas, to recover from Flanary an amount he allegedly owes on a partnership note. The suit was docketed as number 582,448, styled Reynolds, Shannon, Miller, Blinn, White & Cook v. Donald Flanary. Flanary filed an answer in that suit and discovery proceeded. On February 5, 1992, Flanary filed suit against Reynolds, Shannon in the 336th District Court of Grayson County. In that suit, Flanary sought a declaratory judgment that he was not a partner in Reynolds, Shannon; that the Reynolds, Shannon partnership agreement was not effective as to him; and that he has no financial liability to anyone under any agreement made by Reynolds, Shannon. Flanary obtained service of process on Reynolds, Shannon in the Grayson County suit on August 28, 1992, over half a year later.
Reynolds, Shannon filed a plea in abatement with the Grayson County district court asserting that the Harris County county court had acquired prior dominant jurisdiction over the parties and the subject matter. The Grayson County district court overruled Reynolds, Shannon's plea in abatement and signed the August 27, 1993 temporary injunction: (1) compelling Reynolds, Shannon to withdraw anything it had pending in the Harris County county court; and (2) enjoining it from proceeding in any way with any discovery, pleadings, motions, notices, hearings or trials in the suit pending in Harris County except to advise the Harris County county court of the temporary injunction and to request that the court take no action. The August 27, 1993 temporary injunction also set the Grayson County suit for trial on the merits on October 15, 1993.
Reynolds, Shannon timely perfected this appeal from the Grayson County district court's August 27, 1993 temporary injunction. Simultaneously, Reynolds, Shannon also filed a motion for leave to file a petition for writ of mandamus with this Court.

THE MANDAMUS PROCEEDING
Reynolds, Shannon sought a writ of mandamus ordering the Grayson County district court to set aside its August 27, 1993 temporary injunction, to vacate its order overruling Reynolds, Shannon's plea in abatement and to sign an order abating the Grayson County suit. Its petition for writ of mandamus, however, indicated that Reynolds, Shannon had perfected an interlocutory appeal from the temporary injunction. We denied Reynolds, Shannon's motion for leave to file petition for writ of mandamus because we can give it no more relief by mandamus than we can through the interlocutory appeal.
The Supreme Court of Texas has held that mandamus will lie to determine the question of dominant jurisdiction if a second court interferes with an action first filed in another court of coordinate jurisdiction.[2]See Curtis v. Gibbs, 511 S.W.2d 263, 267 (Tex. 1974). Mandamus relief will not lie, however, to determine dominant jurisdiction between two courts when both courts have jurisdiction to act and neither court is interfering with the other's exercise of jurisdiction. See Abor v. Black, 695 S.W.2d 564, 567 (Tex.1985). In effect, a party possesses an adequate remedy by appeal, after a final judgment, from the second court's incidental ruling overruling the plea in abatement. See Abor, 695 S.W.2d at 567.
The supreme court has also held that mandamus will not lie to determine a party's claim that a trial court has no subject matter jurisdiction. Generally, the cost and delay of pursuing an appeal will not, in themselves, render appeal an inadequate alternative to mandamus review. Bell Helicopter Textron, Inc., v. Walker, 787 S.W.2d 954, 955 (Tex.1990) (per curiam). When two courts compete for jurisdiction over the same parties and the same subject matter, the party aggrieved by the second court's assertion of *251 jurisdiction, without more, has an adequate remedy on appeal, despite its cost and delay. See Wyatt v. Shaw Plumbing Co., 760 S.W.2d 245, 246-48 (Tex.1988) (determining on appeal whether the trial court abused its discretion in overruling a plea in abatement when it was not the court of dominant jurisdiction). In this case, Reynolds, Shannon contends that the Grayson County district court erroneously asserted jurisdiction over the suit filed before it. Assuming that Reynolds, Shannon is correct in this assertion, its remedy is by appeal.
In this case, however, the Grayson County district court is not merely competing with the jurisdiction of the Harris County county court; the Grayson County district court has affirmatively enjoined Reynolds, Shannon from proceeding any further in Harris County. It has been held that "[r]emedy by mandamus is available to resolve a conflict in jurisdiction between courts of coordinate jurisdiction only when the trial court first taking jurisdiction has been stopped from proceeding (e.g., when the second court enjoins the parties from taking any more action in the first court)." Allstate Ins. Co. v. Garcia, 822 S.W.2d 348, 349 (Tex. App.San Antonio 1992, orig. proceeding) (citing Abor, 695 S.W.2d at 567, and Gibbs, 511 S.W.2d at 267). When the second court, however, has issued a temporary injunction enjoining the parties from proceeding further in the first court, before it has entered a final judgment containing a permanent injunction within it, the aggrieved party's remedy is by interlocutory appeal. See TEX.CIV.PRAC. & REM.CODE ANN. § 51.014(4) (Vernon Supp. 1993).
We conclude that Reynolds, Shannon has an adequate remedy by appeal after a final judgment for its complaint that the Grayson County district court erroneously asserts jurisdiction over the suit filed by Flanary. To the extent that Reynolds, Shannon complains that the Grayson County district court abused its discretion by issuing a temporary injunction enjoining it from proceeding in Harris County, its remedy is by an accelerated, interlocutory appeal.[3] Accordingly, Reynolds, Shannon had an adequate remedy by appeal for the complaints it raised in its motion for leave and petition for writ of mandamus. As a result, we summarily denied Reynolds, Shannon's motion for leave to file a petition for writ of mandamus.[4]
We did, however, on our own motion, accelerate the briefing schedule of this accelerated appeal. See TEX.R.APP.P. 42(b). We ordered this appeal submitted without oral argument on October 12, 1993. See TEX. R.APP.P. 75(f).

THE ACCELERATED APPEAL
In its fifth point of error, Reynolds, Shannon contends that the Grayson County district court abused its discretion by granting Flanary's motion for a temporary injunction because Flanary has an adequate remedy at law. We agree.
The grant or refusal of a temporary injunction is ordinarily within the sound discretion of the trial court and, on appeal, review of the trial court's action is limited to the question of whether the action constituted a clear abuse of discretion. Priest v. Texas Animal Health Comm'n, 780 S.W.2d 874, 875 (Tex.App.Dallas 1989, no writ). Among the grounds for relief that a successful applicant for injunctive relief must demonstrate is the existence of irreparable injury. Priest, 780 S.W.2d at 875. "Irreparable injury" is stated to be "an injury of such nature that the injured party cannot be adequately compensated therefor[] in damages, or that the damages which result therefrom cannot be measured by any certain pecuniary standard." Canteen Corp. v. Republic of *252 Tex. Properties, Inc., 773 S.W.2d 398, 401 (Tex.App.Dallas 1989, no writ).
The only evidence that the trial court heard concerning Flanary's suffering "irreparable injury" was that the same subject matter, between the same parties, was being litigated in both Grayson County and Harris County. Flanary argues that the Harris County court has no subject matter jurisdiction over the litigation because it entails an accounting of a partnership and the court in Harris County is a county court at law and not a district court.[5] We have concluded, however, that Reynolds, Shannon has an adequate remedy on appeal to complain of the Grayson County district court's assertion of jurisdiction over the litigation. The same reasoning applies to Flanary's argument: he has an adequate remedy on appeal to complain of the Harris County county court's assertion of jurisdiction. Without any showing that he would suffer injury consisting of more than the cost and delay of pursuing an appeal, Flanary has not shown that he will suffer irreparable injury absent injunctive relief. Bell Helicopter Textron, Inc., 787 S.W.2d at 955. Because Flanary has not shown irreparable harm absent injunctive relief and because he has an adequate remedy at law for any jurisdictional ruling that the Harris County county court makes adversely to him, the trial court abused its discretion in granting him injunctive relief. We sustain Reynolds, Shannon's fifth point of error.
In light of our disposition of this point of error, we do not reach Reynolds, Shannon's remaining points of error. We expressly do not decide whether the Harris County county court has subject matter jurisdiction over this litigation. That issue was never raised for the Harris County court's consideration and, more importantly, we have no appellate jurisdiction over a Harris County court. See TEX.GOV'T CODE ANN. § 22.220(a) (Vernon 1988) (limiting jurisdiction of a court of appeals to cases "within its district"); TEX. GOV'T CODE ANN. § 22.201(f) (Vernon 1988) (defining the district as "the counties of Collin, Dallas, Grayson, Hunt, Kaufman, Rockwall, and Van Zandt"). We also do not decide today whether the Grayson County district court has dominant jurisdiction over the subject matter of the parties' dispute; that question is not yet ripe for decision.
Having sustained Reynolds, Shannon's fifth point of error, we reverse the trial court's judgment and dissolve the August 27, 1993 temporary injunction.
NOTES
[1]  The injunction similarly enjoins William E. Junell, Jr., Michael K. Swan, the law firm of Watkins & Watkins, and Bruce K. Watkins, attorneys either affiliated with Reynolds, Shannon or representing Reynolds, Shannon in the Harris County court. We refer to appellants collectively as Reynolds, Shannon throughout this opinion.
[2]  We recognize that the Grayson County court is a district court and that the Harris County court is a county court. Strictly speaking, therefore, the competing courts in this case are not courts of entirely coordinate jurisdiction. Nevertheless, both courts have suits concerning the same subject matter and parties before them, so that the principle of dominant jurisdiction still applies. See Hartley v. Coker, 843 S.W.2d 743, 745-46 (Tex.App.Corpus Christi 1992, no writ) (one suit pending in a county court exercising probate jurisdiction; the other suit pending in a district court).
[3]  Reynolds, Shannon argued in the petition for writ of mandamus that, if Flanary beats it to judgment in Grayson County, Flanary might persuade the Harris County court that the Grayson County judgment is res judicata of any determination that it could make in the matter. We declined to speculate how the Harris County court might react to such an argument.
[4]  Reynolds, Shannon filed a Petition for Leave to File Writ of Mandamus in the supreme court. On October 4, 1993, the supreme court stayed the action in the Grayson County court. On November 17, 1993, the supreme court vacated its October 4, 1993, stay order and denied Reynolds, Shannon's Motion for Leave to File Writ of Mandamus.
[5]  Shannon, Reynolds points out that, although Flanary filed a motion to transfer venue from Harris County to Grayson County, he never obtained a ruling on the motion, nor has he ever filed a plea to the jurisdiction of the Harris County county court.
