  In this paper, we consider the dynamical zeta functions of Ruelle and Selberg
associated with the geodesic flow of a compact hyperbolic odd dimensional
manifold $X$. These functions are initially defined on one complex variable $s$
in some right half-plane of $\mathbb{C}$. Our goal is the continue
meromorphically the dynamical zeta functions to the whole complex plane, using
the Selberg trace formula for arbitrary, not necessarily unitary,
representations $\chi$ of the fundamental group. First, we prove a trace
formula for the integral operator
$D^{\sharp}_{\chi}(\sigma)e^{-t(D^{\sharp}_{\chi}(\sigma))^{2}}$, induced by
the twisted Dirac operator $D^{\sharp}_{\chi}(\sigma)$ on $X$. Then we use
these results to establish the meromorphic continuation of the dynamical zeta
functions to $\mathbb{C}$.
