The activity of Co-zeolites with MFI, BEA, FER, MOR topologies was studied in ethane and propane oxidative dehydrogenation and ammoxidation in a through-flow arrangement and temperature range 350-500degreesC. The products of oxidative dehydrogenation of paraffins were corresponding olefins, CO and CO2, in the propane reaction only a small part was cracked to ethylene and methane. Besides CO and CO2, the ammoxidation of ethane yielded ethylene and acetonitrile, and of propane brought propylene and acetonitrile too. Presence of ammonia increased substantially the paraffin conversion as well as selectivity and yield of the sum of olefin and nitrile for CoH-BEA and CoH-MFI zeolites, while with CoNa-zeolites the paraffin conversion and selectivity were similar. The sequence in activity in both the oxidative dehydrogenation and ammoxidation (in TOF values per Co ion in conversion of paraffins and yields of olefin and olefin+acetonitrile) of Co-zeolites (more pronounced for ammoxidation) Co-BEA > CoMFI much greater than Co-MOR > Co-FER is ascribed to the location of prevailing amount of Co ions in beta cationic position of pentasil ring zeolites, i.e. at the exposed site at the intersection of straight and sinusoidal channel in ZSM-5, and in open channels of beta-zeolite, in contrast to Co-beta ions in MOR and FER structures occurring in the narrow interconnected channels and in eight-member ring channel, respectively. Formation of acetonitrile at propane ammoxidation can be attributed to interaction of ammonia with double bond of propylene at P position, as suggested in literature, as well as to the observed easy decomposition of acrylonitrile to acetonitrile in the presence of ammonia.