Dispersion relations for the mutual scattering of two spin-half particles are proved by studying the analytic and asymptotic properties in the complex energy plane of the outgoing wave Green function of the Hamiltonian. The interaction considered is the most general spin-dependent potential which is invariant under rotations, space reflection, time reversal and Galilean transformations and is no more than linear in the relative momentum: the necessary asymptotic behaviour of each of the four terms in such a potential is examined. The generalization of the results to particles of higher spin is discussed.