DALLAS — Profits are soaring at the biggest U.S. airlines as fuel prices drop — but don’t expect fares to fall too.

Heading into the busy holiday-travel period, the airlines expect even cheaper fuel, thanks to the nosedive in crude oil prices. The price of jet fuel, an airline’s biggest single expense, has dropped by about one-fifth since mid-June.

Airlines are also benefiting from continued strong travel demand that allows them to push fares higher. Executives report strong bookings for holiday travel and say Ebola headlines don’t seem to be scaring away travelers.

The four largest U.S. airlines sold at least 83 percent of their seats in the third quarter. A decade ago, more than a quarter of seats went empty.

The results were there to see Thursday, as several leading airlines reported financial results for the third quarter, which includes the end of the heavy summer-vacation travel season:

The world’s biggest airline operator, American Airlines Group, earned an all-time best $942 million profit in the June-through-September quarter, nearly double the amount that American and US Airways earned separately last year before their December 2013 merger. CEO Doug Parker predicted more records for fourth-quarter and full-year earnings.

United Continental Holdings posted net income of $924 million, up from $379 million a year earlier. Excluding one-time items, adjusted profit was a record $1.1 billion.

Southwest Airlines said profit rose 27 percent to $329 million, and executives said November and December bookings looked good.

All three companies beat Wall Street expectations for earnings.

United cut its fuel bill by $135 million compared with last year, and Southwest saved $64 million.

And that is just the beginning. Those savings are based on what fuel cost in 2013 and don’t include the big decline in prices since June. Southwest paid $2.94 per gallon in the third quarter but predicts it will spend between $2.70 and $2.75 per gallon in the fourth quarter.

Airlines for America, a trade group for the biggest carriers, estimates that every penny decline in fuel prices saves the industry $190 million. That suggests the carriers could save more than $10 billion if fuel stays at current prices.

Airlines could share that windfall with passengers in the form of cheaper tickets, but that doesn’t look likely, at least not yet. The big airlines just pushed through a modest fare increase — $4 for U.S. round-trip tickets.