Two of the biggest U.S. airlines reported record profits for the second quarter, but said they planned to reduce expansion plans for later this year as demand has weakened.

United Continental Holdings Inc., the No. 2 U.S. carrier by traffic, and Southwest Airlines Co., No. 4, both reported sharp jumps in earnings that showed how cheap fuel has helped compensate for lackluster revenue. A third major carrier, Alaska Airlines parent Alaska Air Group Inc., also reported a stellar second quarter.

After several years of strong results helped by tightly limiting increases in flights, U.S. carriers this year have expanded relatively rapidly. That growth has dented unit revenues, the closely watched measure of how much they take in for each passenger flown per mile. The decline has worried investors and depressed airline shares in recent months.

Despite the increases in numbers of seats, critics claim the airlines are restricting capacity to keep prices high. The U.S. Department of Justice is investigating whether the four largest carriers—which include American Airlines Group Inc., the biggest U.S. carrier, and Delta Air Lines Inc., the No. 3—have colluded to limit their expansion. The airlines have denied that, and said that they will continue adjusting plans separately based on their reads of market conditions. Alaska isn't among them.

United on Thursday said it plans to trim its capacity in the second half of 2015 in its core energy markets, in Brazil and across the Atlantic. For the full year, United expects its capacity to rise between 1% and 1.5%, a more modest increase than some of its smaller U.S. competitors. Southwest said it would expand by 7% this year, down from an earlier forecast of up to 8%.

Delta also trimmed its growth forecast when it reported results last week. American reports results on Friday.

Cheaper fuel in the latest quarter compared with a year ago reduced the industry's second-largest expense after labor. United's profit rocketed up 51% from a year ago to $1.2 billion, its best quarterly profit in history, even as revenue shrank 4% to $9.9 billion. Unit revenue fell by a steeper 5.6%, and United forecast a 5% to 7% decline for the current period.

United also announced a new $3 billion share buyback program.

Jim Compton, United's chief revenue officer, attributed the decline in unit revenues to the strong U.S. dollar, price-cutting, and the removal of fuel surcharges on international routes. United, which has a big hub in Houston and carries many workers in the oil and gas industries, said revenue from that sector declined 30%—owing to weak oil prices. But the airline said the decline "has roughly leveled out" and more deterioration isn't expected this year.

Southwest said profit increased 31% to an record of $608 million, while revenue rose 2% to $5.1 billion. Planes were slightly fuller despite a 7% increase in capacity. But Southwest's unit revenue was down 4.6%, and it expects a 1% decline in the current quarter.

Southwest signed a new credit-card agreement that is forecast to add $400 million in revenue in the second half. And after returning $430 million to shareholders in the second quarter, the carrier is accelerating a plan for another $500 million share buyback.

Southwest Chief Financial Officer Tammy Romo also said early indications in the current quarter suggest demand is strengthening. "Revenue trends appear to be stabilizing and improving," she said. Ms. Romo said the new credit-card agreement is a big factor in the current quarter's improved revenue outlook.

Alaska Air Group's profit rose 42% to $234 million, on revenues of $1.44 billion, up 5%. Its unit revenue dipped 5.3% in the second quarter. It didn't give guidance.

United said it would complete its $1 billion stock buyback in the current quarter, nearly two years early, by purchasing about $230 million in shares. The new $3 billion buyback program, which represents 14% of United's market capitalization, is slated to be completed in 2017. Jeff Smisek, the chief executive, said it "demonstrates the confidence we have in our future."

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