An improved process is provided for the production of nitriles from hydrocarbons by reaction with oxygen, air or a gas enriched in oxygen relative to air, preferably the latter, and ammonia in the presence of an ammoxidation catalyst. An alkane, e.g., propane, is converted to an alkene in a catalytic dehydrogenator. The product stream is introduced into an ammoxidation reactor. The product formed therein is recovered in a conventional quench tower. The gaseous effluent from the quench tower is treated in a PSA unit comprising at least two pairs of adsorptive beds. The first bed forms a gas stream containing the unreacted alkane and alkene as well as a minor amount, typically 1-2 percent by volume, of oxygen and a vent stream containing oxygen, nitrogen if present, and hydrogen. The vent stream is introduced into the second adsorptive bed to thereby form an oxygen-containing stream which also contains, nitrogen, if present, and a hydrogen-enriched stream. The oxygen-containing stream may be recycled to the ammoxidation reactor depending on the nitrogen content thereof. The alkene/alkane stream plus at least a portion of the hydrogen stream is introduced into a selective oxidation unit to remove the remaining oxygen and then recycled to the dehydrogenator. The remainer of the hydrogen-enriched stream, if any, may be taken as product or vented. The dehydrogenator may be a multistage dehydrogenator wherein the product stream is withdrawn from a reactor other than the first and last reactors, the recycle streams are introduced into the next sequential reactor and the effluent from the last reactor is introduced into the first reactor, a reactor having a similar alkane composition or directly into the admmoxidation/oxidation reactor.