The plaintiff physicians appeal from the second grant of summary judgment entered by the district court in this antitrust suit. The plaintiffs’ original action essentially alleged that the emergency room procedures instituted by the defendant hospitals constituted a successful conspiracy to eliminate the plaintiffs from emergency room practice and to monopolize local emergency services in violation of sections 1 and 2 of the Sherman Antitrust Act, 15 U.S.C. §§ 1, 2.1 The district court first granted *1174summary judgment for the defendants on the ground the plaintiffs had failed to submit sufficient evidence of a conspiracy, combination or actual restraint of trade to sustain a prima facie violation of sections 1 and 2.2
On appeal, this Court affirmed the district court’s grant of summary judgment on the plaintiffs’ conspiracy claims under sections 1 and 2 but reversed and remanded the section 2 monopolization and attempted monopolization claims against the defendant Burns Clinic for further consideration.3 The Clinic thereupon renewed its motion for summary judgment before the district court claiming that the plaintiffs had failed to properly define a relevant market or produce evidence of antitrust injury. On remand, the district court found the plaintiffs had presented insufficient evidence to support the elements of the section 2 claims against the Clinic. The court entered an unpublished order granting summary judgment for the Clinic on March 1, 1984. We affirm the district court judgment for the reasons set forth below.
The facts of this case are fully set forth in this Court’s first opinion, Smith v. Northern Michigan Hospitals, Inc., 703 F.2d 942, 945 (6th Cir.1983). In June 1977, the Little Traverse and Lockwood-MacDonald Hospitals in Petoskey, Michigan merged to create former defendant Northern Michigan Hospitals, Inc. (NMH).4 Pri- or to the merger, the plaintiffs, independent physicians affiliated with the staff of the former Lockwood-MacDonald facility, had practiced family medicine in Petoskey and had provided emergency room services for the facility on a rotating part-time basis.
After the merger, the following changes in the hospitals’ operations occurred: the plaintiffs became staff members of NMH; the emergency rooms of the two former facilities were consolidated; and NMH abolished the rotational use of independent physicians for emergency room staffing and instituted a policy requiring staffing by full-time acute care specialists. The policy also called for follow-up care of emergency patients to be referred to independent doctors or specialists on NMH’s staff. To procure the acute care specialists, NMH solicited bids for an exclusive contract from the defendant Burns Clinic, independent physicians in Petoskey and a private acute care corporation. The plaintiff physicians did not submit a bid. NMH subsequently awarded the exclusive contract for emergency care to Burns Clinic which agreed to refer uncommitted emergency room patients to NMH’s independent general-practitioners, including the plaintiffs, or to its specialists.
The plaintiffs filed suit contending that the exclusive contract and the referral system, which they alleged yielded them few patients, constituted an unreasonable restraint on trade in violation of section 1 and a conspiracy to monopolize emergency medical care in the Petoskey market in violation of section 2. ,On appeal from the district court’s initial grant of summary judgment, this Court ruled that the district court properly granted summary judgment for the defendants on all conspiracy claims and dismissed NMH as a defendant in the suit. However, the Court remanded the *1175section 2 claims for further factual development- of the relevant discernible market.5 On remand, the district court granted the remaining defendant, Burns Clinic, summary judgment on the section 2 claims. The court found minimally sufficient evidence that the relevant product market consisted of the overlap between the family services the plaintiff physicians are permitted by NMH to cover and the same services offered by the specialists of Burns Clinic. The district court then defined the relevant geographic market as the three county area from which most of the plaintiffs’ patients came prior to the merger. The court proceeded to find that although the Clinic possessed a monopoly share of the secondary (acute) care market, the plaintiffs had failed to show the extent to which NMH’s primary care monopolized the overlap market or the extent to which primary care services at NMH were performed by the Clinic’s staff. The district court further found from the defendant’s affidavits 6 that a number of independent physicians had established practices in Petoskey since the merger. The district court concluded the plaintiffs had failed to present preliminary evidence showing the Clinic’s general intent to monopolize or the elements of a section 2 attempt to monopolize claims: specific intent to monopolize the overlap market, anticompetitive behavior and a dangerous probability of success.
On appeal the plaintiffs contend the district court erred in requiring them to conclusively prove their case to survive the defendant’s renewed motion for summary judgment; and in finding the plaintiffs had failed to preliminarily establish the Clinic’s monopoly power and intent to monopolize. We do not agree.
In its prior opinion, this Court set out the elements of a monopolization and an attempted monopolization violation of section 2 of the Sherman Act:
To establish the offense of monopolization a plaintiff must show that a defendant either unfairly attained or maintained monopoly power. United States v. Grinnell Corp., 384 U.S. 563, 570-71, 86 S.Ct. 1698, 1703-04, 16 L.Ed.2d 778 (1966). Monopoly power consists of “the power to control prices or exclude competition.” Id. at 571, 86 S.Ct. at 1704. An attempted monopolization occurs when a competitor, with a “dangerous probability of success,” engages in anti-competitive practices the specific design of which are, to build a monopoly or exclude or destroy competition. See Times-Picayune Publishing Co. v. Unit*1176ed States, 345 U.S. 594, 627, 73 S.Ct. 872, 890, 97 L.Ed. 1277 (1952); Swift & Co. v. United States, 196 U.S. 375, 396, 25 S.Ct. 276, 279, 49 L.Ed. 518 (1905); E. Kintner, Federal Antitrust Law, Vol. II, § 13.1, p. 406 (1980) (citing cases).
In order to succeed on either a monopolization or attempt to monopolize claim plaintiffs must establish the relevant product and geographic markets in which they compete with the alleged monopolizers. See, e.g., United States v. Grinnell Corp., 384 U.S. 563, 571-73, 86 S.Ct. 1698, 1704-05, 16 L.Ed.2d 778 (1966); Walker Process Equipment, Inc. v. Food Machinery & Chemical Corp., 382 U.S. 172, 177, 86 S.Ct. 347, 350, 15 L.Ed.2d 247 (1965). United States v. E.I. duPont de Nemours & Co., 351 U.S. 377, 395-99, 396 n. 23, 76 S.Ct. 994, 1007-1009, 1008 n. 23, 100 L.Ed. 1264 (1956); Times-Picayune, 345 U.S. at 611-12, 73 S.Ct. at 881-882 (1953).
703 F.2d at 954. While the proof submitted by the plaintiffs is entitled to the more lenient scrutiny accorded proof in antitrust cases on summary judgment, the plaintiffs must nonetheless show some factual basis for their claims. First National Bank of Arizona v. Cities Service Co., 391 U.S. 253, 286-90, 88 S.Ct. 1575, 1591-93, 20 L.Ed.2d 569 (1968). The plaintiffs must also rebut the defendant’s legitimate explanations for the alleged anticompetitive conduct with “significant probative evidence tending to support the complaint.” Id. at 290, 88 S.Ct. at 1593.
In our view, the district court was required to grant summary judgment to the defendant because the plaintiffs had failed to submit probative evidence which would “require a judge or jury to resolve the parties’ differing versions of the truth at trial.” First National Bank, 391 U.S. at 286-90, 88 S.Ct. at 1591-93. We find no error in the district court’s determination that the plaintiffs failed to present evidence establishing the defendant’s primary care practice or the extent to which that practice constituted a monopoly share of the overlap market. Moreover, the plaintiffs submitted no evidence from which the court could infer the defendant’s general intent to monopolize. Nor did the plaintiffs submit evidence to rebut the defendant’s explanations for the small number of post-merger referrals received by the plaintiffs. Absent evidence establishing the defendant’s share of the relevant market and proof from which the district court can infer general intent to monopolize, the plaintiffs’ prima facie case of monopolization cannot withstand even the more lenient antitrust standard for summary judgment.
Even if the plaintiffs could show they were denied a fair share of the referrals, their failure to establish what portion of the overlap market was consumed by the defendant’s referrals precludes finding the elements of an attempt to monopolize claim. Thus, assuming the conduct complained of constituted anticompetitive behavior, the district court did not err in finding insufficient evidence from which to infer the other two elements of an attempt to monopolize claim, the Clinic’s specific intent to monopolize or the dangerous probability that it could have succeeded. We conclude the plaintiffs’ total failure to produce evidence showing the defendant’s share of the market precluded establishment of the plaintiffs’ section 2 claims and required the district court to enter an order of summary judgment for the defendant.
Accordingly, the judgment of the Honorable Richard A. Enslen, is affirmed based upon the reasoning of the district court opinion.
. 15 U.S.C. §§ 1, 2 provides in part:
§ 1. Trusts, etc., in restraint of trade illegal; exemption of resale price agreements; penalty
Every contract, combination in the form of trust or otherwise, or conspiracy, in restraint of trade or commerce among the several Státes, or with foreign nations, is declared to be illegal: ...
Every person who shall make any contract or engage in any combination or conspiracy declared by sections 1 to 7 of this title to be illegal shall be deemed guilty of á misdemean- or, and, on conviction thereof, shall be punished by fine not exceeding fifty thousand dollars, or by imprisonment not exceeding *1174one year, or by both said punishments, in the discretion of the court.
§ 2. Monopolizing trade a misdemeanor; penalty
Every person who shall monopolize, or attempt to monopolize, or combine or conspire with any other person or persons, to monopolize any part of the trade or commerce among the several States, or with foreign nations, shall be deemed guilty of a misdemean- or, and, on conviction thereof, shall be punished by fine not exceeding fifty thousand dollars, or by imprisonment not exceeding one year, or by both said punishments, in the discretion of the court.
. Smith v. Northern Michigan Hospitals, Inc., 518 F.Supp. 644 (W.D.Mich.1981).
. Smith v. Northern Michigan Hospitals, Inc., 703 F.2d 942 (6th Cir.1983).
. This Court dismissed all claims against NMH in its first disposition of this case. Smith v. Northern Michigan Hospitals, Inc., 703 F.2d at 955.
. In determining the plaintiffs’ conspiracy claims, this Court addressed the three anti-competitive practices complained of by the plaintiffs: the exclusive emergency room contract; the discriminatory application of NMH’s emergency room referral system from 1977 to 1979; and the pediatrician rule requiring uncommitted non-traumatic emergency patients 14 years old and younger be referred to pediatricians. This Court determined that the reasons submitted by NMH for awarding an exclusive emergency services contract were "manifestly legitimate”, 703 F.2d at 953, that the adverse affects of such a system were uniform among all NMH doctors, id. at 954, and that the referral system, fair on its face, had not been shown to predominantly channel patients to specialists for illegitimate reasons. Id. at 950. The Court did find, however, that the pediatrician rule could, theoretically, restrain competition between family practitioners and pediatric specialists but that without a properly defined market, evaluation of the rule and the other alleged anticompetitive practices under section 2 of the Sherman Act was not possible. Id. at 955-56.
. The plaintiffs vigorously challenge the district court’s consideration of affidavits filed by the defendant as attachments to a reply brief in support of the defendant’s renewed motion for summary judgment. See Federal Rule of Civil Procedure 6(d). We find no abuse of discretion in the court’s consideration of the affidavits. A district court may, for cause shown, consider affidavits filed after the motion. Eguia v. Tompkins, 756 F.2d 1130, 1136 n. 6 (5th Cir. 1985); 2 J. Moore, Moore’s Federal Practice, ¶ 6.08 (2d Ed.1985); Fed.R.Civ.P. 6(b). In light of the defendant’s need to address the plaintiffs' claims as articulated in the latter’s reply brief in opposition to the defendant’s motion for summary judgment, we cannot conclude the district court erred in considering the defendant's untimely affidavits. The plaintiffs show neither how they were prevented from filing opposing affidavits under Federal Rule of Civil Procedure 56(c), nor why they did not request additional time to file opposing affidavits despite three weeks between the time the defendant filed its reply brief and the date of trial.