  In this paper we consider the Bloch eigenvalues and spectrum of the
non-self-adjoint differential operator L generated by the differential
expression of odd order n with the periodic PT-symmetric coefficients, where
n>1. We study the localizations of the Bloch eigenvalues and the structure of
the spectrum. Moreover, we find conditions on the norm of the coefficients
under which the spectrum of L coincides with the real line
