This invention relates to polyurethane elastomers and to a process for their production. These elastomers comprise the reaction product of a polyisocyanate component comprising an allophanate modified (cyclo)aliphatic polyisocyanate which has an NCO group content of about 15 to about 35% or a prepolymer thereof, with an isocyanate-reactive component comprising a low unsaturation polyether polyols, a low molecular weight organic compound containing two hydroxyl groups and which is free of amine groups, and, optionally, one or more organic compounds having a molecular weight of about 200 to about 500, a hydroxyl functionality of 3 to 4 and comprising an amine-initiated polyether polyol.