DALLAS — For airlines, the record profits keep coming, thanks to cheaper jet fuel.

Like motorists, airlines have been saving money at the pump since oil prices began plunging last summer. Even with a recent increase, the spot price of jet fuel is down 40 percent since September. Airlines are getting such a price break that profits are surging even though their revenue is flat or declining.

At American Airlines, passengers flew fewer miles and revenue declined 2 percent in the first quarter. But thanks to a $1.36 billion cut in its fuel bill, American reported Friday that it earned a record $932 million.

The other three U.S. airline giants reported similar results:

 United Airlines posted record first-quarter earnings of $508 million, even though revenue dipped 1 percent; it saved more than $1 billion on fuel.

 Delta more than tripled its net income to $746 million after spending $600 million less on fuel.

 Southwest tripled its profit to a record $453 million; fuel savings were $437 million.

It’s stunning, considering that the first quarter is usually the weakest of the year for airlines. From 2000 through 2013, the nation’s airlines lost money in the first quarter every year but one, according to government figures.

One reason is that the big airlines have held on to most of their savings from cheaper fuel. They haven’t shared the bounty with passengers through lower fares because travel demand has remained steady and most planes are nearly full at current prices.

The average domestic round-trip ticket sold so far is $454 including taxes, a savings of just $2 from last summer despite the huge drop in fuel prices, according to the Airlines Reporting Corp., which processes ticket transactions for airlines and travel agencies.