  Work is a continuation of work TMPh, 175(2), 2013. We study the Potts model
with zero external field on the Cayley tree. It is shown that for any values of
the parameter all periodic Gibbs measures are translation-invariant for the
q-state antiferromagnetic Potts model on the Cayley tree of order two and for
the q-state ferromagnetic Potts model on the Cayley tree of order k.
