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.

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 still far short of the 17 million annual rates from the late 1990s and early 2000s.

The biggest winner among major automakers was South Korea's Hyundai Motor Co. Its sales skyrocketed 49 percent to 31,005 vehicles. Japan's Nissan Motor Co. came next with a 5.6 percent gain, followed by GM at 4.7 percent, aided by strong pickup 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.