Abstract: Tertiary alkylphosphines of the general formula R.sub.3 P, in which R stands for identical or different, linear, unsubstituted alkyl groups having 3 to 20 carbon atoms, with the proviso however that one of the alkyl groups may be a secondary butyl group, are made by reacting hydrogen phosphide PH.sub.3 with an appropriate alkene or alkenes in stoichiometric excess, if desired, at elevated temperature and under increased pressure in contact with a radical-yielding agent. 2,2'-azobis-(2-methylbutyronitrile) is used as the radical-yielding agent in the absence of whatever alien solvent.