Organic compounds containing at least one site of ethylenic unsaturation are catalytically hydrocyanated and the medium of hydrocyanation is separated into desired linear organic compounds containing at least one nitrile function, e.g., 3-pentenenitrile, and undesired nitrile by-products, e.g., methylglutaronitrile, and the undesired nitrile by-products are hydrodenitrogenated into ammonia and at least one hydrocarbon compound under an absolute hydrogen pressure ranging from 0.1 to 10 MPa at a temperature ranging from 200° to 500° C. and in the presence of a hydrodenitrogenation catalyst.