NEW YORK (CNN/Money) - Southwest Airlines has dismissed two pilots who allegedly removed most or all of their clothes during a flight, according to a published report.

USA Today reports that the two male pilots, who were not identified by the airline, were dismissed for "inappropriate conduct," quoting airline spokeswoman Ginger Hardage.

Southwest "will not tolerate any inappropriate or offensive behavior," she said.

There is no indication that the safety of the flight was affected or that any Federal Aviation Administration regulation was violated.

The paper said the pilots involved are appealing their termination. They contend that one of them removed his uniform after coffee was spilled, according to the paper. A flight attendant saw them after being summoned to the cockpit to bring paper towels and soda water. Southwest is treating the episode as a prank that went too far, the paper said.

Southwest has become the nation's most financially successful airline, partly through good labor relations, which have allowed it to keep its costs and fares lower than competitors'. The paper quotes the airline's pilots union as saying the dismissal and the appeal were "an internal matter."