  Following Part~I, we consider a class of reversible systems and study
bifurcations of homoclinic orbits to hyperbolic saddle equilibria. Here we
concentrate on the case in which homoclinic orbits are symmetric, so that only
one control parameter is enough to treat their bifurcations, as in Hamiltonian
systems. First, we modify and extend arguments of Part~I to show in a form
applicable to general systems discussed there that if such bifurcations occur
in four-dimensional systems, then variational equations around the homoclinic
orbits are integrable in the meaning of differential Galois theory. We next
extend the Melnikov method of Part~I to reversible systems and obtain theorems
on saddle-node, transcritical and pitchfork bifurcations of symmetric
homoclinic orbits. We illustrate our theory for a four-dimensional system, and
demonstrate the theoretical results by numerical ones.
