Epoxy functional copolymers of a higher alpha -olefin, and an unsaturated dicarboxylic acid ester formed by copolymerization of olefin, acid ester and ethylenically unsaturated glycidyl compound can be used to form nitrogen, oxygen, phosphorus and/or sulfur-containing lubricant additives by reaction of the epoxy functionality in such a copolymer with glycidyl-reactive compounds containing nitrogen, oxygen, phosphorus and/or sulfur atoms. Alternatively, the copolymerization reaction can utilize the olefin, unsaturated acid ester, and an ethylenically unsaturated compound containing the nitrogen, phosphorus and/or sulfur atom, which compound is formed by reaction of ethylenically unsaturated glycidyl compound and an epoxy-reactive nitrogen, phosphorus, and/or sulfur-containing compound.