Substantially random ethylene copolymers containing at least 3.0 mole percent of geminally disubstituted olefin monomers are described. The geminally disubstituted olefin monomers can be represented by the generic formula R.sub.1 =R.sub.2 (R.sub.3)(R.sub.4), where R.sub.1 is CH.sub.2, R.sub.2 is C, and R.sub.3 and R.sub.4 are, independently, essentially linear hydrocarbyl groups having from 1 to 30 carbon atoms, or more, and containing one carbon atom bound directly to R.sub.2. The copolymers can be prepared by coordination polymerization by means of contacting at least one geminally disubstituted olefin monomer and ethylene, optionally with one or more other coordination polymerizable monomers, with a catalyst system comprising a monocyclopentadienyl, heteroatom-containing Group 4 transition metal catalyst component.