Investigation of the glass transition temperature (T-g) and the tendency to crystallize in quiescent and stretched modes for hydrogenated acrylonitrile-butadiene rubber (HNBR) are reported. HNBR is a copolymer produced by the selective hydrogenation of the butadiene unit in acrylonitrile-butadiene rubber (NBR). In our consideration, HNBR was treated as a terpolymer of ethylene, acrylonitrile and 1-butene. Comparison of the T-g behavior with other ethylene copolymers indicated that HNBR had T-g behavior typical of ethylene copolymers. Crystallinity developed in low acrylonitrile HNBR through annealing. It was also found that crystallinity developed in HNBR with high acrylonitrile content was due to alternating sequences of acrylonitrile and hydrogenated 1,4 butadiene units.