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ESR spin-probe values of glass temperatures are reported for a series of di-, tri-, and radial block copolymers. With one exception, in which the hard phase is poly(t-butylstyrene), the hard component is polystyrene (PS); the soft components include polybutadiene (PBD), polyisoprene (PI), hydrogenated PBD, hydrogenated PI, and poly(dimethyl siloxane) (PDMS). Tg's of the soft phase are in general agreement with those of the respective high molecular weight homopolymers; Tg's of the hard phase generally deviate widely from those of corresponding high molecular weight homopolymers. This deviation is interpreted in teens of a number of factors, including, the molecular weight of the hard phase, differences in solubility parameters for the two phases, percent of the hard phase present, and the presence of crystallinity. Comparison of Tg's determined by ESR with Tg's from dynamic mechanical methods on S-B-S triblocks of similar composition demonstrates that the ESR method is measuring the Tg of the interpliase and hence, in principle, its composition.