A golf ball comprises a dynamically crosslinked thermoplastic material prepared by a method including: (a) partially crosslinking a rubber composition of a rubber polymer and two free radical initiators at a first crosslinking temperature to form a thermoplastic, partially crosslinked elastomer composition; (b) mixing a thermoplastic polymer composition with the thermoplastic, partially crosslinked rubber composition and heating the mixture to a second crosslinking temperature higher than the first crosslinking temperature and at which the thermoplastic polymer composition is liquid; and (c) continuously mixing the mixture while further crosslinking the rubber composition to form a thermoplastic material having a dispersed phase of crosslinked rubber composition in the thermoplastic polymer composition.