DALLAS — After a decade of multibillion-dollar losses, U.S. airlines appear likely to profit for years for a simple reason: They are flying less.

By grounding planes and eliminating flights, airlines have cut costs and pushed fares higher. As the global economy rebounds, travel demand is rising and planes are as full as they’ve been in decades.

From 2000 through 2009, U.S. airlines lost about $60 billion and eliminated 160,000 jobs, according to an industry trade group, the Air Transport Association.

But now profit margins at big airlines are the highest in at least a decade, according to the government. The eight largest U.S. airlines are forecast to earn more than $5 billion this year and $5.6 billion in 2012.

U.S. airlines are in the midst of reporting fourth-quarter results that should cap the industry’s first moneymaking year since 2007.

“The industry is in the best position – certainly in a decade – to post profitability,” says Southwest Airlines CEO Gary Kelly. “The industry is much better prepared today than it was a decade ago.”

The airlines’ turnaround has benefited investors – the Arca airlines stock index has nearly quadrupled since March 2009 – but it’s been tough on travelers.

Fares in the U.S. have risen 14 percent from a year ago, according to travel consultant Bob Harrell. Flights are more crowded than they’ve been in decades. On domestic flights, fewer than one in five seats is empty. Space is even tighter over the summer and holidays. That’s why it took a week to rebook all the travelers who were stranded by a snowstorm that hit the Northeast over Christmas weekend.

The industry was profitable in 2000, 2006 and 2007, when the economy was roaring. But those boom years masked the industry’s underlying problems, including high costs and too many empty seats. During 2008 and 2009, airlines lost a combined $23 billion, but they were also attacking their problems, setting the stage for a comeback in 2010.