CINCINNATI – Two military fighter jets apparently flew higher than allowed and came so close to a commercial flight over southern Ohio this week that they triggered a cockpit alarm in the commuter plane, authorities said Friday.

Atlantic Southeast Airlines Flight 5202, a 70-seat commuter jet, was flying from Cleveland to Atlanta on Thursday when its two pilots saw the F-16s nearby at 10 a.m., the airline said.

The commercial planes “had a near-miss incident,” said Federal Aviation Administration spokesman Tony Molinaro.

Radar showed the Ohio National Guard F-16s were flying at 30,000 feet when they should have been no higher than 29,000 feet, Molinaro said. The commercial plane was flying as planned at 30,000 feet, he said.

The F-16s are from the 180th Fighter Wing, based at the Toledo Express airport and were on normal training flights, said Mark Wayda, a spokesman for the Columbus-based Guard. The Guard is investigating, he said.

“It does appear they were above their ceiling, but we are not sure by how much at this point,” he said.

The commercial pilots saw the F-16s but couldn’t say how near they came, Molinaro said. Pilots contacted controllers, who cleared them to climb to 36,000 feet as a precaution.

The plane was carrying 58 passengers and four crew members; it remained on its flight plan and landed safely and on time, said Kate Modolo, spokeswoman for the Atlanta-based Atlantic Southeast.

“Our pilots did a good job and handled the flight appropriately and got our passengers safely to Atlanta,” she said.

A pilot does not often get outside the training area, Wayda said. If the investigation results warrant, procedures will be reviewed and the F-16 pilots involved could be retrained, he said.

“There are not many of these sort of near-miss incidents,” he said.

The sight of jet fighters outside a plane’s window can mean they’ve been sent because of an air security or safety concern, but that apparently wasn’t the case this time.

“That was not a NORAD mission,” John Cornelio, spokesman for the North American Aerospace Defense Command, said.