Anti-wear and high pressure lubricating compositions with a major proportion of lubricating oil and a minor proportion of at least one amine phosphate containing a terminal imide ring result from the reaction, under conditions for the formation of an amine salt, of at least one phosphate having the general formula (I): ##STR1## in which n is equal to 1 or 2, R.sup.1 is a divalent hydrocarbon group with 1 to 32 carbon atoms, R.sup.6 represents a hydrogen atom or a monovalent hydrocarbon group containing usually from 1 to 200 carbon atoms, with at least one amine.