After years of trouble in Europe, General Motors Co.’s (NYSE: GM) sales turned sharply higher in January, outpacing the region’s overall performance. The results, driven by results of GM’s Opel/Vauxhall division, rose 13.7% to 58,387. Total passenger car registrations in the European Union rose 6.7% to 999,157.

GM, however, has lost so much market share that its piece of the EU passenger cars was only 6.1% of the total last month, according to the European Automobile Manufacturers Association. (The GM share includes a small number of sales by Chevy.) That means GM trails smaller arch rival Ford Motor Co. (NYSE: F) at 6.9% and even niche luxury car company BMW at 6.4%.

Volkswagen continues to hold an extraordinary portion of European sales, at 238,698 for January. It has 25% of the market. By contrast, GM has about 18% of its home market in the United States.

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The second largest manufacturer in Europe, PSA Group, which makes Peugeot, had 11.1% of the market in the EU in January, another measure of how dominant VW is with over twice the share. In third place, Renault Group had a 9.3% share.

The January numbers show how well luxury car manufacturers have done. Aside from BMW, Daimler, maker of Mercedes, had a market share of 6%. The two Germany companies are also the two top-selling luxury brands in the United States.

European car sales remain critical to global manufacturers because the region is one of the three huge markets along with the United States and China. Ironically, while VW thrives in Europe, it continues to wither in the United States. VW only sold 23,504 cars in America in January, which gave it a market share near 2%. Without strong U.S. sales, VW has little chance of becoming the dominant global car company.

On the other hand, without a sharp increase in market share in Europe, GM faces challenges of its own as it tries to fend off Toyota Motor Corp. (NYSE: TM) and VW worldwide.

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