Compounds containing at least one nitrile functional group are produced by hydrocyanation of an organic compound having at least one site of non-conjugated unsaturation, having from 2 to 20 carbon atoms, by reaction with hydrogen cyanide in the presence of a catalytic system containing a complex of nickel having the oxidation state of zero with at least one organophosphorus ligand selected from the group consisting of organophosphites, organophosphonites, organophosphinites and organosphosphines and a cocatalyst of the Lewis acid type of formula: in which M1 and M2 are each elements selected from the group consisting of zinc, boron, aluminum, cadmium, gallium, indium and tin.