(FORTUNE Magazine) - Stuttgart, Germany German automakers are world-renowned for putting design in motion. Now their most breathtaking concepts are standing still: Mercedes, BMW, and Porsche are each opening showpiece museums featuring gleaming lines, curves, glass, innovative architecture--and, of course, cars that don't move.

First to the flag is Mercedes, which opened its $192 million shrine, the Mercedes-Benz Museum, in May. The building, designed by Dutch firm UN Studio, took eight years from drawing board to opening. It takes visitors on a twisting, double-helix pathway through 16,500 square meters of display space and 120 years of Mercedes history, beginning with the invention of the first gas-powered automobile by Gottlieb Daimler and Karl Benz in 1886.

BMW is scheduled to open its museum, BMW World, in Munich next spring, and Porsche's entry in Stuttgart will open soon after. All three are big, beautiful, and expensive ads--cathedrals to auto engineering. But they arrive as many carmakers are ailing; Mercedes cut 8,500 jobs last fall.

Along with a number of new auto factories, including Volkswagen's "glass factory" in Dresden and architect Zaha Hadid's BMW plant in Leipzig, they can be seen as either costly arrogance or faith in the future. In the meantime, the German automakers are expecting big crowds. Mercedes says one million people a year will walk through its Guggenheim Museum-inspired spiral showcase, and Porsche is expecting 200,000 visitors a year.