Compositions for golf balls that include polyurethane and polyurea linkages and that are crosslinked in the soft segments of the polymer backbone. In particular, the compositions of the invention, which are based on a polyurethane and/or polyurea prepolymers, have improved crosslink density from the crosslinking between the soft, unsaturated segments of the polymer backbone. The curative blend includes at least one isocyanate-reactive component and a free radical initiator.