Disclosed is a selected type of copolymer composition comprising copolymers having units derived from ethylene and dicyclopentadiene (DCPD) co-monomers. Such copolymer compositions: a) have a DCPD-derived comonomer unit content of from about 25 mole % to about 45 mole %; b) have a Weight Average Molecular Weight, Mw, of greater than about 170,000; c) comprise amorphous material and have glass transition temperatures, Tg, of from about 8° C. to about 129° C., which also fit the equation Tg (in ° C.)≧[(mole % DCPD×3.142)−4.67]; and d) comprise no significant amount of crystalline polyethylene homopolymer or crystallizable polyethylene segments within the ethylene-dicyclopentadiene copolymers. Such copolymers can be readily derivatized by hydrogenation and/or epoxidation to provide polymeric materials suitable for use as engineering thermoplastics. Also disclosed are processes for preparing and optionally further derivatizing ethylene/dicyclopentadiene copolymers having the characteristics hereinbefore described.