The Supreme Court on Tuesday questioned a massive sex discrimination lawsuit on behalf of at least 500,000 women claiming that Wal-Mart favors men over women in pay and promotions.

The justices suggested that they are troubled by lower court decisions allowing the class-action lawsuit to proceed against the world's largest retailer.

Justice Anthony Kennedy, often a key vote on the high court, said he is unsure "what the unlawful policy is" that Wal-Mart engaged in to deprive women of pay increases and promotions comparable to men.

Billions of dollars are at stake in the case. Class actions create pressure on businesses to settle claims and create the potential for large judgments.

Wal-Mart denies it discriminates against its female employees.

But Joseph Sellers, the lawyer for the women, said that lower courts were persuaded by statistical and other evidence put forth so far in the 10-year-old lawsuit.

Sellers said a strong corporate culture at Wal-Mart's Bentonville, Ark., headquarters that stereotyped women as less aggressive than men translated into individual pay and promotions decisions at the more than 3,400 Wal-Mart and Sam's Clubs stores across the country.