Appellant’s motion for stay pending appeal of the district court’s April 2, 1992, order is denied. The court’s order enforces the Internal Revenue Service’s (IRS) sum *323 mons requiring the appellant to appear, to testify, and to produce certain records, papers, and other data in her possession relevant to the determination of the tax liabilities of certain John Doe taxpayers. Appellant appeals that order contesting the court’s determination that she is barred from challenging the IRS’ compliance with the statutory provisions authorizing issuance of the summons, under 26 U.S.C. § 7609(f)(2) (1988), at the enforcement hearing to show cause for her noncompliance with the summons. Appellant now requests that we stay the district court’s April 2, 1992, order pending the outcome of her appeal.

Our standard of review in cases of this sort is well-settled. The grant of a motion to stay the trial court’s mandate is an exceptional response granted only on a showing of “a probable likelihood of success on the merits on appeal,” or upon a lesser showing of a “ ‘substantial case on the merits’ when ‘the balance of the equities weighs heavily in favor of granting the stay.’ ” Garcia-Mir v. Meese, 781 F.2d 1450, 1453 (11th Cir. 1986) (quoting Ruiz v. Estelle, 650 F.2d 555, 565 (5th Cir. 1981), cert. denied, 460 U.S. 1042, 103 S.Ct. 1438, 75 L.Ed.2d 795 (1983)). Appellant neither has demonstrated a probable likelihood of success on the merits on appeal, see United States v. John Mutschler & Assoc., Inc., 734 F.2d 363 (8th Cir. 1984), United States v. Samuels, Kramer and Co., 712 F.2d 1342 (9th Cir. 1983), Agricultural Asset Management Co., Inc. v. United States, 688 F.2d 144 (2d Cir. 1982); but see United States v. Brigham Young University, 679 F.2d 1345 (10th Cir. 1982), nor that the balance of equities weighs heavily in favor of granting the stay.

Accordingly, appellant’s motion for stay of the district court’s April 2, 1992, order is DENIED.