The present invention relates to a process for producing compounds comprising at least one nitrile function by hydrocyanation of a compound comprising at least one non-conjugated unsaturation.The invention proposes a process for producing compounds comprising at least one nitrile function by hydrocyanation of an organic compound comprising at least one non-conjugated unsaturation, comprising from 2 to 20 carbon atoms, by reaction with hydrogen cyanide in the presence of a catalytic system comprising a complex of nickel having the oxidation state of zero with at least one organophosphorus ligand chosen from the group comprising organophosphites, organophosphonites, organophosphinites and organosphosphines and a cocatalyst of the Lewis acid type.