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The eigenfrequencies associated to a damped wave equation on a compact Riemannian manifold are known to belong to a band parallel to the real axis. Under the assumption of periodicity of the geodesic flow we study the asymptotic distribution of the eigenfrequencies inside the band. We show that the eigenfrequencies form clusters determined by the Morse index of the closed geodesics and the damping coefficient averaged along the geodesic flow. The asymptotics for the multiplicities of the clusters are obtained.