  We study self-adjoint bounded Jacobi operators of the form:
  (J \psi)(n) = a_n \psi(n + 1) + b_n \psi(n) +a_{n-1} \psi(n - 1) on
$\ell^2(\N)$. We assume that for some fixed q, the q-variation of $\{a_n\}$ and
$\{b_n\}$ is square-summable and $\{a_n\}$ and $\{b_n\}$ converge to q-periodic
sequences. Our main result is that under these assumptions the essential
support of the absolutely continuous part of the spectrum of J is equal to that
of the asymptotic periodic Jacobi operator. This work is an extension of a
recent result of S.A.Denisov.
