  In this paper, we study the Selberg and Ruelle zeta functions on compact
hyperbolic odd dimensional manifolds. These zeta functions are defined on one
complex variable $s$ in some right half-plane of $\mathbb{C}$. We use the
Selberg trace formula for arbitrary not neccesarily unitary representations of
the fundamental group to establish the meromorphic continuation of these zeta
functions to the whole complex plane.
