A process for producing aromatic or heterocyclic nitriles, which comprises reacting an alkyl-substituted aromatic hydrocarbon or an alkyl-substituted heterocyclic compound with ammonia and oxygen in the presence of a catalyst composition comprising (a) at least one composite oxide selected from the group consisting of a binary composite oxide comprising titanium and silicon, a binary composite oxide comprising titanium and zirconium and a ternary composite oxide comprising titanium, silicon and zirconium, and (b) an oxide of at least one metal selected from the group consisting of vanadium, molybdenum, tungsten, chromium, antimony, bismuth, phosphorus, niobium, iron, nickel, cobalt, manganese and copper.