The invention relates to reaction membranes that contain a selective oxidation catalyst disposed on a ceramic membrane that selectively conducts oxide ions and that is composed of (Sr1-xCax)1-yAyMn1-zBzO3-δ, wherein A represents Ba, Pb, Na, K, Y, an element of the lanthanide group or a combination of these elements, B represents Mg, Al, Ga, In, Sn, an element of the 3d or 4d period or a combination of these elements, x is a number of from 0.2 to 0.8, y is a number of from 0 to 0.4, z is a number of from 0 to 0.6 and δ is a number that results from the principle of electroneutrality on the basis of x, y and z. The inventive reaction membranes are suitable for use in oxidative reactions of hydrocarbons in which oxygen is used.