For pt. I see ibid., vol.7, no.5, 572 (1974). The general theory of the scattering of two particles in a time-dependent external field, presented in paper I, is applied to the case of two point particles with internal structure which interact through a potential with matrix representation (Vkl(r)). Under suitable, quite general, conditions upon the l2 operator bound mod V(r) mod of (Vkl(r)) the existence of the wave operators Omega +or-(s) is proven for two field configurations. The first is that of a spatially homogeneous time-dependent field, whereas in the second case the field is inhomogeneous but localized in space. Some attention is paid to the problem of the existence of differential cross sections and their relation to the scattering operator S(s)= Omega *+(s) Omega -(s).