A thermoplastic polyurethane or polyurea elastomer made by reacting in a "one-shot" process a polyether diol, a diisocyanate, and a difunctional, isocyanato-reactive chain-extender, the polyether diol being prepared utilizing a double metal cyanide complex catalyst and having a molecular weight of between about 2000 and about 20,000, said diol having an end group unsaturation level of no greater than 0.04 milliequivalents per gram of diol, the equivalent ratio of NCO groups on said diisocyanate to active hydrogen groups on said diol plus chain extender being between about 1:0.7 and about 1:1.3, and the molar ratio of chain extender to diol being between about 0.15:1 and about 75:1.