A sex discrimination suit against Wal-Mart on behalf of at least 500,000 past and present female employees appeared to be on the verge of unraveling at the U.S. Supreme Court on Tuesday, as conservative justices questioned the rationale for holding the retail giant accountable for store-level decisions.

In particular, Justice Anthony Kennedy, who often casts the deciding vote in close cases, said the women's claims seemed contradictory. The plaintiffs said on the one hand that Wal-Mart was infused with sex bias, Kennedy said, and on the other hand that the company provided no standards to store managers who made the personnel decisions.

"It seems to me there's an inconsistency there, and I'm just not sure what the unlawful policy is," Kennedy said during the one-hour argument.

The women's lawyer, Joseph Sellers, replied that the only contradiction was between Wal-Mart's professed policy of nondiscrimination and its practice of paying women less than men and promoting them less often.

The Wal-Mart suit was filed in San Francisco by six women nearly a decade ago. Lower courts have certified it as a class action on behalf of female employees who have worked at the chain's retail stores and Sam's Club warehouses since December 1998.