Compositions for golf balls that include polyurethane and/or 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, have improved crosslink density and hardness 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.