DETROIT — After months of roller-coaster results, the U.S. auto industry showed signs of stability in October.

Total sales of cars and light trucks were unchanged at just over 838,000 compared with October of last year, but rose 12 percent from a dismal September 2009, Autodata Corp. reported Tuesday. The results signaled that some consumers are starting to spend again and the sputtering economy is beginning to pull out of trouble.

“It’s ... a fairly stable kind of footing that the industry is getting under it,” said Gary Dilts, a former Chrysler sales executive who is now senior vice president of global automotive operations for J.D. Power and Associates.

Last month’s sales, if projected for an entire year, rose to 10.5 million after slumping to 9.2 million in September, the month after the government’s Cash for Clunkers rebates ran out. Analysts said the figures are good for a normally weak October, but they’re still far short of the 17 million annual rates from the late 1990s and early 2000s.

“Clearly we’re seeing improvement in the economy and in the industry. It isn’t huge, but it’s a good sign given that Cash for Clunkers is over,” said Mike DiGiovanni, General Motors Co.’s executive director of global market and industry analysis.

The biggest winner among major automakers was South Korea’s Hyundai Motor Co., which saw sales skyrocket 49 percent to 31,005 vehicles, boosted by the Elantra small sedan. Japan’s Nissan Motor Co. came next with a 5.6 percent gain, followed by GM at 4.7 percent, aided by strong pickup truck sales, the performance of new models and the highest incentives in the industry. It was GM’s first year-over-year monthly sales increase in 21 months.

Toyota Motor Corp. said its sales edged up less than a percent, while Honda sales were flat. Less-rosy news came from Chrysler Group LLC, whose sales fell 30 percent, though they improved from September.

Ford Motor Co.’s sales rose 3 percent and it gained U.S. market share for the 12th time in 13 months as its critically acclaimed vehicles continue to grab buyers from rivals. Ford has benefited from consumer goodwill because it didn’t take government bailout money or go into bankruptcy protection, as General Motors and Chrysler did.

But there are ominous signs that could continue to drag down auto sales.

The jobless rate hit a 26-year high of 9.8 percent in September and is expected to rise to 9.9 percent when the October rate is released Friday. Consumer confidence continued to deteriorate last month amid pessimism about future earnings and worries the economic climate would worsen in the next few months.

Emily Kolinski Morris, Ford’s top economist, said uncertainty will continue as long as employment keeps declining, but she said October sales show a real underlying demand for new vehicles after the distorting effects of the clunkers program during July and August. Clunkers offered up to $4,500 rebates for people who traded in older models for more fuel efficient vehicles.

The economy, Kolinski Morris said, is in transition from recession to recovery with financial markets improving.

And the auto industry still has to see its way through a number of economic challenges, said Bob Carter, a Toyota vice president.

“We expect the recovery to be very gradual, extending into next year and beyond,” he said.

GM was obviously concerned about its incentive spending, with new sales chief Susan Docherty saying that the company had to bring the numbers down. GM spent $4,100 per vehicle last month as it paid to phase out the Saturn and Pontiac brands. It also had to unload a large number of 2009 pickup trucks.

In October, 52 percent of GM’s sales were 2009 models, 47 percent were new 2010s and one percent were from 2008. By contrast, 80 percent of Ford’s sales were 2010 models.

GM, Docherty said, plans to reduce incentives as it sells down older models and ships more newly launched vehicles.

Despite GM’s spending, industrywide incentives were down about $100 per vehicle compared to September, said Jesse Toprak, chief analyst for the car-pricing Web site TrueCar.com.

He expects incentives will continue to drop in November before rising again at the holidays in December.

He also said that as GM winds down Pontiac and Saturn, eliminating the need for incentives on those vehicles, he expects GM and other automakers to start pricing cars closer to what they’ll sell for instead of relying so heavily on incentives.

“Eventually, the product has to sell itself,” he said.