For American Airlines, sorry seems to be the hardest word.

The nation's biggest airline placed ads in newspapers around the country Wednesday apologizing for poor holiday service and accusing its pilots union of encouraging an illegal sickout.But the ad got the name of the union wrong, forcing a second apology.

"We most sincerely apologize for wrongfully identifying the Air Line Pilots Association when we should have said Allied Pilots Association," said American chairman Robert Crandall in a letter to ALPA president Randolph Babbitt.

ALPA represents pilots of Eastern, United and other airlines. The union, bsaed in Herndon, Va., said the ad had damaged its reputation and it demanded a correction, which Crandall said American would provide in future ads.

Bill Walters, a spokesman for the Allied Pilots Association, which represents American's pilots, said the mistake is "indicative of the ineptness of management at American."

The union and airline have tried for 15 months to write a new five-year contract for one that expired Jan. 1, 1990.

"The pilots continue to be saddened and angry that the management of American Airlines will continue to blame their management difficulties on the professional pilots of the Allied Pilots Association," Walters said of the ad placed in The Wall Street Journal and newspapers at American's hub and crew base cities.

Under the headline "AApology," American hinted that healthy pilots were calling in sick and said it was taking steps to prevent further service disruptions.

"Most of our 100,000 employees . . . are embarrassed by our temporary inability to serve you properly during the holidays," the ad said.

American canceled 1,460 flights from Friday to Tuesday when an abnormally high number of its 8,700 pilots said they were sick and unable to work. The carrier blamed crew problems for 831, or 57 percent, of the scrubbed flights.

American has about 2,200 daily flights.

"There is no organized activity," said Walters, who is also an American pilot. "There was none called for. There's been none conducted."

Delays and cancellations affected 60,000 passengers during the five days, the airline estimated. There was no estimate of revenue lost by the disruptions.

The count of American pilots who were out sick on some days reached 500, more than twice the average, said company spokesman John Hotard.