FORT WORTH, Texas — American Airlines executives should have been celebrating last week during their annual stockholders' meeting, the first in six years at which they could spotlight an annual profit.

FORT WORTH, Texas — American Airlines executives should have been celebrating last week during their annual stockholders' meeting, the first in six years at which they could spotlight an annual profit.

Instead, chief executive Gerard Arpey spent much of the session fending off questions from irate employees. After agreeing to accept massive pay cuts in recent years to keep American flying, the employees said they were upset that the carrier's top officers have been given stock-based bonuses worth millions of dollars. One employee at the meeting called Arpey and other executives "arrogant, greedy, selfish and heartless individuals."

The anger has not been directed at only American's leaders. Employees who have taken pay cuts at United and Northwest airlines and US Airways are battling their executives over similar deals. Labor groups say the unhappiness has led to at least two showdowns with managers over contractual issues. Some say demoralized workers could hurt service.

"When you have a bitter and angry work force, that translates into a rough-and-tumble summer travel season," said Edward Wytkind, president of the AFL-CIO's Transportation Trades Department, an umbrella organization that lobbies on behalf of airline unions.

The executives and their representatives all defended the deals, saying the bonuses were granted for solid performance. The companies say much of their executives' compensation is in the form of stock grants, which could drop if the airlines perform badly. They also note that the companies' boards set the compensation levels.

During American's annual stockholder meeting, Arpey said the $160 million in stock awards given to top executives and managers was a motivational tool that helped keep the carrier out of bankruptcy.

Arpey, who made a little more than $6 million last month when he sold his stock awards, noted that the carrier preserved its workers' pensions and that employees also have benefited from rising stock prices. They were given 38 million stock options in 2003.

"This may be an issue on which we may have a hard time finding common ground," Arpey told the shareholders and workers.

Other airline bosses are reaping bonuses for helping turn carriers around. Glenn Tilton, United's chief executive, last year received 545,000 shares of United stock — worth about $20 million — that will vest over four years. He was granted more than 800,000 stock options, which could prove lucrative if the carrier's stock price climbs.

Northwest, which was granted court approval last week to exit bankruptcy protection, announced recently that its chief executive, Douglas Steenland, received stock and options worth more than $20 million that will vest over four years. Meanwhile, Douglas Parker, chief executive of US Airways, was given cash bonuses and stock grants worth about $4.8 million last year, according to SEC filings.

Worried about employee reaction to the payout at a time of slumping performance, Parker sent workers an e-mail last month to address why "many of you are wondering how I could be paid so much when our airline is doing so poorly right now."

The bonuses are already resulting in labor disputes.

Last month, United's pilots voted overwhelmingly to reject a deal that would have allowed some pilots to fly extra hours each month during the busy summer and fall travel seasons. A spokesman for the union said the vote reflected anger over executive compensation.

American's pilots last year torpedoed the carrier's high-profile bid to win a lucrative nonstop route to China by refusing to fly longer hours. Union representatives have said in news reports that pilots were upset in part about stock grants to the company's leadership.

Analysts said the executive compensation deals are not outrageous compared with those given by other large companies but come at a bad time for the airlines.

"The whole idea of the last couple years was to create new cultures at airlines that would keep costs down," said Darryl Jenkins, an aviation consultant. "These very large executive payouts are going to end up costing airlines an enormous amount of money. The employees are going to want their fair share."

Jenkins noted Delta's chief executive, Gerald Grinstein, turned down pay packages when his carrier exited bankruptcy protection a few weeks ago and Continental's executives last year turned down $23 million in stock incentives. Those moves helped build goodwill with employees, Jenkins said.