
750 S.W.2d 177 (1988)
DOCTORS HOSPITAL FACILITIES, d/b/a Doctors Hospital et al., Petitioners,
v.
FIFTH COURT OF APPEALS et al., Respondents.
No. C-6577.
Supreme Court of Texas.
May 18, 1988.
R. Brent Cooper and Michael W. Huddleston, Cowles & Thompson, Robert A. Gwinn and Kenneth C. Stone, Gwinn & Roby, Dallas, for petitioners.
W. James Kronzer, Houston, Douglas D. Mulder, Dallas, Ronald D. Krist, Krist, Gunn, Weller, Neumann & Morrison, Houston, John H. Hagler, Dallas, for respondents.
WALLACE, Justice.
The issue in this original proceeding is whether a court of appeals has the power to rule upon a party's timely filed motion for rehearing, after an application for writ of error has already been filed by the opposing party. Relators, collectively referred to as Doctors Hospital, were the Appellees in a cause before the Fifth Court of Appeals, and are the Respondents in that same cause now pending in this court. Rose v. Doctors Hospital Facilities, 735 S.W.2d 244 (Tex.App.-Dallas 1987, writ granted). Doctors Hospital has filed a Petition for Writ of Mandamus, requesting us to compel the lower court to rule upon its Motion for Rehearing so that we may pass upon the points of error raised in that motion. We conditionally grant the writ.
On February 9, 1987, the court of appeals issued two opinions in this cause, one published and one unpublished. See 735 S.W.2d at 245. In the unpublished opinion, the court reversed a judgment n.o.v. in favor of Doctors Hospital and rendered *178 judgment on the jury verdict, subject to suggested remittiturs by the plaintiffs. Both parties filed timely motions for rehearing. The motion filed by Doctors Hospital was overruled. The court sustained one of the four points of error in the Roses' Motion for Rehearing, and overruled the remaining three. After the Roses had filed the suggested remittiturs, the court rendered a new judgment.
After rendition of this judgment, Doctors Hospital filed a Second Motion for Rehearing, complaining that the court should have remanded the cause for a new trial because the Roses had filed "conditional remittiturs." However, before the court of appeals had ruled upon Doctors Hospital's Second Motion for Rehearing, the Roses filed an Application for Writ of Error. In an unpublished order, the court of appeals held that the Motion for Rehearing should be dismissed for want of jurisdiction. Apparently, the court of appeals was of the opinion that the filing of an application for writ of error wholly divested it of jurisdiction over the cause. Cf. Johnson v. Sovereign Camp, W.O.W., 125 Tex. 329, 83 S.W. 2d 605, 607-8 (1935).
This court has no jurisdiction of a party's application for writ of error unless and until a motion for rehearing has been filed in and overruled by the court of appeals. Oil Field Haulers Ass'n v. Railroad Commission, 381 S.W.2d 183, 187 (Tex.1964). Further, we are precluded from considering a point of error not presented in such a motion to the lower court. TEX.R.APP.P. 131(3). Each time the court of appeals vacates one judgment and substitutes another, a party affected by the subsequent judgment is entitled to and should file another motion for rehearing. Stoner v. Massey, 586 S.W.2d 843, 845 (Tex.1979); Bain Peanut Co. of Texas v. Pinson & Guyger, 119 Tex. 572, 34 S.W.2d 1090 (1931). If an error should occur on or after a rehearing in that court, a subsequent motion for rehearing must be filed in order to preserve the error for consideration by this court. Stoner, 586 S.W.2d at 845; Bain Peanut, 34 S.W.2d at 1091.
Doctors Hospital's complaints regarding the nature of the Roses' remittiturs did not arise until after its First Motion for Rehearing had been filed and the Roses had filed their remittiturs. Thus, it was incumbent upon Doctors Hospital to raise these complaints in a Second Motion for Rehearing, if it sought to invoke this court's jurisdiction over those complaints. Since Doctors Hospital filed the Second Motion for Rehearing in a timely manner, it did everything required of it to ensure that its right to appeal to this court would not be lost. See TEX.R.APP.P. 100(a) (Vernon 1988). Yet, according to the court of appeals, Doctors Hospital was deprived of this right simply because the opposing parties availed themselves of it first.
There are three requisites for a mandamus: a legal duty to perform a nondiscretionary act, a demand for performance, and a refusal. We have previously held that mandamus will lie to compel a clerk of a court of appeals to file a motion for rehearing if a motion is timely presented to the clerk and filing is denied. Stoner, 586 S.W.2d at 846 and authorities cited therein. Since Doctors Hospital filed a timely motion for rehearing and the court of appeals has refused to rule upon it, there can be no question that there has been both a demand for performance and a refusal. The sole inquiry is whether the court below had a legal duty to rule upon the motion.
In Stoner, we held that a court of appeals has no authority to refuse a litigant the right to file a motion for rehearing. 586 S.W.2d at 846; see also Cowan v. Fourth Court of Appeals, 722 S.W.2d 140 (Tex.1987). If a party has the right to file a motion for rehearing in the court of appeals, and that court has no discretion to deny that right, then surely it must follow that the court cannot refuse to rule upon it. Since a timely motion for rehearing must be both filed and overruled by the court of appeals before our jurisdiction will attach, the right to file a motion for rehearing would be without any value whatsoever if the court had no duty to act upon it. That duty is clearly expressed in TEX.R.APP.P. *179 100(c), which dictates that the court of appeals shall either grant or overrule the motion, depending upon its view of the merits.
However, it is equally clear that a court has no power, and hence no duty, to rule upon a matter over which it has no jurisdiction. The issue thus depends on whether the court of appeals had jurisdiction to rule upon the motion for rehearing after the Roses had filed their application. If the court retained such jurisdiction, then it was under a mandatory duty to exercise it. If it lacked such jurisdiction, it could take no further action.
We hold that the court of appeals had jurisdiction to rule upon Doctors Hospital's Motion for Rehearing, notwithstanding the fact that an application for writ of error had been filed. In so holding, we recognize that when an application for writ of error is filed in this court, this court generally acquires jurisdiction over the case to the exclusion of all other courts. Ammex Warehouse Co. v. Archer, 381 S.W.2d 478, 482 (Tex.1964). We also acknowledge the general principle that a lower court has no power to vacate or change its judgment in a case, after the plenary jurisdiction of a higher tribunal has attached. Robertson v. Ranger Ins. Co., 689 S.W.2d 209, 210 (Tex.1985); Carrillo v. State, 480 S.W.2d 612, 616 (Tex.1972). However, there is no basis for applying these principles to the situation presented in this case.
The rules expressed in Ammex, Robertson and Carrillo rest upon the more basic principle that one court should not interfere with the jurisdiction of another, especially when the latter is a higher tribunal. This principle is, of course, necessary to the orderly and efficient administration of justice. However, justice is not served by a rule that allows one litigant to deprive the other of the right to invoke the appellate jurisdiction of this court, merely by invoking it first. Moreover, a ruling by the court of appeals on Doctors Hospital's Second Motion for Rehearing would not interfere with the jurisdiction of this court. In fact, such a ruling would facilitate and indeed provide a necessary predicate for the exercise of our jurisdiction, since we have no power to rule upon the matters required to be raised in that motion in the absence of such a ruling. Oil Field Haulers, 381 S.W.2d at 187. With respect to the points Doctors Hospital was required to raise in a second motion for rehearing, our jurisdiction simply has not attached. Therefore, there is no basis for applying the rule expressed in the above cases, and we can perceive no reasonable purpose that would be subserved by sanctioning the result of the court of appeals' holding.
We have long recognized that the right of access to an appellate tribunal is a valuable one, constitutionally protected against arbitrary or unreasonable abrogation. Dillingham v. Putnam, 14 S.W. 303 (Tex. 1890). To be sure, our rules of appellate procedure place some restrictions upon that right, but these restrictions are valid in that they serve to provide a more orderly and efficient judicial system. However, when the general rule that a lower court can take no further action after our jurisdiction has been invoked is applied to the facts of this case, the result is an unreasonable and arbitrary denial of a litigant's right of appellate review. The court of appeals' express holding was that it had no jurisdiction to rule upon Doctors Hospitals' complaints, and the end result of that holding is that we have no jurisdiction to rule upon these matters either. In light of the foregoing analysis, this holding is not in consonance with the constitutionally protected right of access to an appellate court. TEX. CONST. art I, § 13.
We recognize that language in Johnson v. Sovereign Camp, W.O.W., countenances the result reached by the court of appeals. However, that case has been rightly criticized as "obviously unjust." Ratcliff v. National County Mutual Fire Ins. Co., 745 S.W.2d 75, 77 (Tex.App.-Dallas 1988, writ dism'd w.o.j.). We overrule Johnson, to the extent that it conflicts with our decision in this case.
In light of our opinion today, we are confident that the court below will vacate its order dismissing Doctors Hospital's Motion *180 for Rehearing for want of jurisdiction. The writ of mandamus will issue only if the court fails to do so. Action in Rose v. Doctors Hospital Facilities, C-6535, will be held in abeyance pending final disposition of the Motion for Rehearing in this matter by the Fifth Court of Appeals.
