The Geneva Auto Show opens in Switzerland this week. It’s usually a glitzy affair, but while U.S. carmakers are on the rebound, gloom has descended on the European auto industry. Car sales in Europe have plunged as a result of the economic crisis, and that’s a big problem for European carmakers.

In the auto business, Philippe Houchois, an analyst at UBS, says there’s a very important rule to live by: “Cars become stale after a while.”

In other words, you need new models, and that’s what car shows are for.

General Motors is unveiling a new convertible Corvette in Geneva, but David Bailey of Coventry University says struggling European automakers don’t have much to show this year.

“It could cost up to a billion dollars to get a genuinely new car to market,” says Bailey. “So it’s hugely expensive.”

With cars sales in Europe at a 17-year low, there’s little money to spend on innovation.

France’s Peugeot and Renault have presented revamped, SUV-style models, but Houchois says the risk is that as profits drop further, European manufacturers will fall into a downward spiral — less investment means fewer new cars. 

“And over time, you drop off the shopping list of car buyers,” says Houchois. He says that presents an opportunity for U.S. carmakers and others to snatch up European customers.