A system which is suitable as a catalyst for the hydrocyanation of olefinically unsaturated compounds and comprises a) Ni(0) b) a compound which complexes Ni(0) as a ligand and contains trivalent phosphorus, c) a Lewis acid and d) a compound of the formula M Rn where M: Al or Ti R: identical or different monovalent alkoxy radicals, in which case a plurality of alkoxy radicals may be bonded together, and additionally, in the case that M=Al, R may be identical or different monovalent alkyl radicals, in which case a plurality of alkyl radicals may be bonded together or one or more alkyl radicals may be bonded to one or more of the abovementioned alkoxy radicals, n: valency of M, and processes for hydrocyanating an olefinically unsaturated compound in the presence of such a system.