Process for preparing styrene, and an appropriate agent

A process for oxidatively dehydrogenating ethylbenzene to prepare styrene, which process comprises reacting ethylbenzene in the vapor phase with oxygen at a temperature above 350.degree. C. in the presence of a crystalline zirconium phosphate catalyst capable of ion exchange, said zirconium phosphate catalysts having been precipitated in a gel-like form from a zirconium salt solution by the addition of an excess of phosphate ions, impregnated with at least 1 liter of an at least 10 M orthosphophoric acid per 100 g of zirconium phosphate gel, filtered off from excess phosphoric acid, washed with water until the water draining off has a pH of 2 to 3 and dried at 120.degree. to 250.degree. C.