Supreme Court justices questioned the underpinnings of a massive class-action lawsuit against Wal-Mart on Tuesday and whether female employees could show that a common, discriminatory policy governed the company’s pay and promotion decisions.

Even justices who seemed sympathetic to letting the largest gender discrimination lawsuit in history proceed to trial had questions about how it might go forward.

Lawyers for women suing the nation’s largest retailer built their case on affidavits from more than 100 workers and a statistical model showing that, while women make up 80 percent of the company’s hourly workers, they account for only 30 percent of its managers. They allege pay discrepancies, unequal promotion policies and a male-dominated management.

But some justices said they had trouble understanding how, in the plaintiffs’ view, Wal-Mart carried out its policy of discrimination.

“It’s not clear to me: What is the unlawful policy that Wal-Mart has adopted, under your theory of the case?” asked Justice Anthony M. Kennedy, often the key vote on a divided court.

Joseph M. Sellers, a Washington lawyer who argued the case on behalf of Wal-Mart greeter Betty Dukes and other women, said Wal-Mart allowed great discretion to local managers to make pay and personnel decisions.

But he said the Bentonville, Ark.-based company instilled in those managers a sense of “the Wal-Mart way” that was used to “pay women less than men who were doing the same work in the same facilities at the same time . . . and provided fewer opportunities for promotion.”

Kennedy was not satisfied.

“Your complaint faces in two directions. Number one, you said this is a culture where Arkansas knows, the headquarters knows, everything that’s going on,” Kennedy said. “Then in the next breath, you say, well, now these supervisors have too much discretion. It seems to me there’s an inconsistency there.”

Justice Antonin Scalia quickly picked up the theme.

“I’m getting whipsawed here,” Scalia said. “On the one hand, you say the problem is that they were utterly subjective, and on the other hand you say there is a — a strong corporate culture that guides all of this. Well, which is it?”

The questions echoed Wal-Mart’s argument that lower courts should not have certified a class-action suit against the company, because hiring practices and anecdotal evidence of discrimination cannot be tied to the company, which has an official policy of nondiscrimination.

“If the three named plaintiffs stand before the court, they are supposed to represent 500,000 or a million or more people,” said Theodore J. Boutrous Jr., who represented Wal-Mart. “And the claim is that the individual decision-makers in those other cases exercised their discretion in a way that was biased, and there’s no proof of that.”

The issue before the court is not whether Wal-Mart is guilty of discrimination, but whether the women suing the company have made a compelling case that a jury should hear the issue.

The court’s liberals stressed that point, and said that simply adopting a policy of nondiscrimination was not enough to insulate Wal-Mart from liability.

Justice Ruth Bader Ginsburg said that even a company with such a policy must ask itself whether it is being enforced if the company receives reports “month after month” that women are underrepresented in managerial jobs and lag in pay.

“Isn’t there some responsibility on the company to say, is gender discrimination at work, and if it is, isn’t there an obligation to stop it?” Ginsburg asked.

Boutrous replied that Wal-Mart’s study showed no pay discrepancies between men and women at 90 percent of the company’s stores.

Justice Elena Kagan said she was “a little bit confused as to why excessive subjectivity is not a policy that can be alleged” as a discriminatory practice.

And Justices Sonia Sotomayor and Stephen G. Breyer reminded that if the suit were allowed to go forward, Wal-Mart would have a chance to prove the allegations false.

“Ultimately, you may win and prove to a fact-finder that this analysis is fatally flawed,” Sotomayor said, but that does not mean the justices should overturn the decision of a federal judge and the U.S. Court of Appeals for the 9th Circuit that the case should be heard.

But even Sotomayor and Ginsburg expressed concern about the suit. Sotomayor worried that using the plaintiffs’ statistical model to award back pay would limit the company’s right to defend against specific allegations.

And Ginsburg said she had a “very serious problem” with the way back pay, damages, and injunctive relief from Wal-Mart’s allegedly discriminatory practices were all raised in the same class action.

That could lead to a narrow decision in which the court separated the issues and sent the case back to lower courts.

But other justices had concerns beyond the procedural. Chief Justice John G. Roberts Jr. and Justice Samuel A. Alito Jr. asked, in effect, whether Wal-Mart is any different from other large companies.

Alito wondered whether a company would be in violation of civil rights laws if the disparities in its workforce were typical of other companies. Roberts ventured that Wal-mart might even be a little better.

“Is it true that Wal-Mart’s pay disparity across the company was less than the national average?” Roberts asked Sellers.

The lawyer replied that the issue was not how Wal-Mart ranked.

“Wal-Mart’s obligation . . . is to ensure that its managers do not make pay decisions because of sex, and the comparison that’s relevant is between men and women at Wal-Mart, not the general population,” Sellers said.

The case is Wal-Mart Stores Inc. v. Dukes . A decision could come any time before the court adjourns in late June.