DETROIT – General Motors has strung together a tidy three-year run of profits by making big dollars in its backyard.

Now the question is whether its U.S. operations can keep making enough to carry the company and cover widening losses in Europe.

General Motors Co. on Thursday posted a profit of $4.9 billion for 2012, down 36 percent from a year earlier, when it made $7.6 billion. Its net income fell because of European losses and a truckload of one-time accounting gains and losses in both years. Last year’s pretax profit, which excludes the one-time items, still dropped, but only by 5 percent to $7.9 billion. Revenue for the year rose 1 percent to $152.3 billion.

The company’s money machine, North America, made $6.9 billion before taxes for the year. But GM lost almost $1.8 billion in Europe, where it has too many factories and workers as sales slow in a faltering economy.

The European losses widened by more than $1 billion. They also wiped out the combined $1 billion made by GM’s auto loan and South American businesses, plus part of the $2.2 billion made by International Operations including China. GM expects the European market to weaken further this year, which could further stress its bottom line.

Just about every automaker is seeing sales fall and losses mount in Europe as the economy there continues to unravel. And GM’s use of U.S. profits to cover the losses isn’t unique. Its chief rival, Ford Motor Co. posted a record North American pretax profit of $8.3 billion last year, but it lost $1.75 billion in Europe.

Still, GM executives are optimistic that cost-cutting and 23 new vehicles by 2016 will help Europe break even before taxes by the middle of this decade. They said new pickup trucks, two new Cadillacs and other new models will keep profits rolling in the U.S.

“The GM launching these products is undeniably a stronger company than it was even a year ago,” CEO Dan Akerson said.

The automaker has a truck assembly plant in southwest Allen County and a foundry in Defiance, Ohio.