Two proxy advisers recommended Exxon Mobil Corp. and Chevron Corp. shareholders vote in favor of splitting the chairman and CEO roles, creating a potential flashpoint with the boards at the oil giants’ annual meetings on May 27.

Glass Lewis & Co. and Egan-Jones Proxy Services say investors should vote against the companies and embrace proposals that would create independent chairs once the incumbents -- Darren Woods at Exxon and Mike Wirth at Chevron -- step down. Both advisory firms say that a CEO who also leads the board raises a potential conflict of interest.

“An independent chair is better able to oversee the executives of a company and set a pro-shareholder agenda without the management conflicts that a CEO or other executive insiders often face,” Glass Lewis said in its report on Exxon.

Last year, almost 41 per cent of Exxon investors voted in favor of the proposal, which would amount to one of the biggest corporate governance changes in Exxon’s history if passed.

Legal & General Investment Management, the U.K.’s largest asset manager and a top 20 Exxon shareholder, said it will vote in favor of the proposal, and also plans to vote against Woods’s re-election over what it called a lack of ambition over climate change. The California Public Employees’ Retirement System, America’s largest state public pension fund, and the New York State Common Retirement Fund have also said they support splitting the chairman and CEO roles.

Institutional Shareholder Services Inc., another big proxy adviser, said investors should reject the CEO-chairman split at Exxon and Chevron, calling the powers of lead directors at both companies “robust.”

Exxon recently beefed up the responsibilities of its lead director to address some shareholder concerns. In its proxy filing, Exxon said that having the CEO chair the board ensures “ensures items of greatest importance for the business are brought to the attention of, and reviewed by, the board on a timely basis.” In another filing on Wednesday, the company rejected Glass Lewis’s stance on the separation of the roles, pointing out that 90 per cent of its board is independent and that only about 34 per cent of S&P 500 companies have an independent chairman.

Chevron said having a CEO-chairman can be an advantage when negotiating oil and gas deals with host countries and that re-electing directors annually enhances its shareholder oversight.