And Institutional Shareholder Services and Glass, Lewis, the influential proxy advisory firms, are advising clients to vote against certain board members based on the active bribery inquiry and other issues and advocating support of the United Automobile Workers’ proposal.

The board’s failure to reassure shareholders that the alleged violations of the foreign bribery law “will have a limited impact on shareholder value, and that any responsible executives will be appropriately held accountable, calls into question the ability of the company’s leaders to protect shareholders’ investments,” I.S.S. wrote in its report on the company.

The New York Times reported in April of last year that officials at Wal-Mart de Mexico, a subsidiary, had bribed authorities to ease expansion in that country and that executives at the company’s headquarters in Bentonville, Ark., had been alerted to the bribery and declined to take action. The company is conducting an internal investigation into potential violations of the Foreign Corrupt Practices Act, and it is being investigated by the Securities and Exchange Commission and the Department of Justice.

Last year, about one-third of nonfamily-member shareholders voted against four directors — Michael T. Duke, the chief executive; H. Lee Scott, a former chief executive; S. Robson Walton, the chairman; and Christopher Williams, the chairman of the audit committee. Including family member votes, the opposition exceeded 12 percent, the biggest opposition any had faced in years and the biggest vote against a sitting chief executive in recent company history. This year, the board and company are again under fire, as advocates say the company needs to improve transparency surrounding the investigation, among other issues.

Investors “remain in the dark as to the nature and extent of the alleged violations (and knowledge of them within the company); as to the nature of any past or future sanctions for executives with direct responsibility or oversight responsibility; and even as to the timetable for completion of the investigation and disclosure of its results,” I.S.S. wrote in a report.

Citing those concerns, I.S.S. recommended that shareholders vote against the re-election of S. Robson Walton, Mr. Duke and Mr. Williams.

Randy Hargrove, a company spokesman, noted that Wal-Mart had made several changes to its compliance program in the last year and a half. It improved the way it reported and investigated accusations of ethical violations; it hired new executives to oversee compliance; and it combined its compliance, ethics, investigations and legal functions into one department, he said.