The invention relates to a process of the oxidative dehydrogenation of an alkane containing 2 to 6 carbon atoms and/or the oxidation of an alkene containing 2 to 6 carbon atoms, wherein oxygen, water and the alkane and/or alkene are fed to a reactor and are contacted with a mixed metal oxide catalyst containing molybdenum, vanadium, niobium and optionally tellurium in the reactor, and wherein the molar ratio of water as fed to the reactor to oxygen as fed to the reactor is smaller than 1:1.