The present invention relates to a process of hydrocyanation of ethylenically unsaturated organic compounds to compounds having at least one nitrile function, particularly the hydrocyanation of diolefins such as butadiene, or of substituted olefins such as alkene nitrites such as pentenenitriles; the subject hydrocyanation is carried out in the presence of a catalytic system comprising a metallic element and mono- and pluri-dentate organophosphorus ligands.