By Tom Hals

WILMINGTON, Del. (Reuters) - Big pension funds have been fighting for years to hold Wal-Mart's board of directors liable for covering up a purported bribery scandal in Mexico.

The outcome of the case turns in part on an unusual question: if a top judge offers unsolicited legal advice to plaintiffs, is it negligent to ignore it?

The case stems from an investigation by The New York Times in 2012 over allegations that Wal-Mart Stores Inc, the largest U.S. retailer, covered up $24 million in bribes paid by its Mexican subsidiary to build stores.

A federal investigation is underway, and Wal-Mart has said it is cooperating with authorities.

California State Teachers’ Retirement System, or CalSTRS, and New York City pension funds sued Wal-Mart in Delaware, where the retailer is incorporated, with allegations that the board members failed to investigate the bribery, which Wal-Mart has denied. The funds brought what is known as a derivative lawsuit, and typical of such cases, the funds are seeking governance changes.

Earlier this year, a nearly identical case in Arkansas was dismissed for procedural reasons.

Wal-Mart on Thursday asked the Delaware court to dismiss the pension fund case, saying it would be unfair for the retailer to face the allegations twice.

The pension funds' lawyer, Stuart Grant, countered that the funds should not be bound by the Arkansas case, which he claimed was so poorly handled it amounted to negligence.

Grant reminded the court on Thursday that the first judge to handle the Delaware case had warned shareholders they would lose without a thorough investigation first. The Delaware shareholders heeded the warning and have spent three years fighting for documents, and the Arkansas shareholders did not. Delaware law applied in both cases.

"One of the top jurists is telling people you're foolish to move forward with that case in Arkansas," said Delaware Court of Chancery's chief judge, Andre Bouchard, at Thursday's hearing. Bouchard asked Wal-Mart's lawyer: "Why isn't that grossly deficient?"

Theodore Boutrous, the lawyer for Wal-Mart, argued that qualified lawyers handled the Arkansas case, which he said was dismissed because Wal-Mart's board acted properly.

Leo Strine was originally assigned to the Delaware case. He was later promoted to the Delaware Supreme Court and Bouchard took over the Wal-Mart case.

Strine had warned in a July 2012 hearing that a case against Wal-Mart would fail if shareholders did not make targeted allegations that some board members knew of the bribery scheme and concealed it.

(Reporting by Tom Hals in Wilmington, Delaware; editing by Grant McCool)