  We study the number of the poles of the meromorphic continuation of the
dynamical zeta functions $\eta_N$ and $\eta_D$ for several strictly convex
disjoint obstacles satisfying non-eclipse condition. We obtain a strip $\{z \in
\mathbb C:\: {\rm Re}\: s > \beta\}$ with infinite number of poles. For
$\eta_D$ we prove the same result assuming the boundary real analytic.
Moreover, assuming the abscissa of convergence of the series (1.5} negative,
for $\eta_N$ we obtain a characterisation of $\beta$ by the pressure $P(2G)$ of
some function $G$ on the space $\Sigma_A^f$ related to the dynamical
characteristics of the obstacle.
