  It is shown that there is a generalization of the Conley-Zehnder index for
periodic trajectories of a classical Hamiltonian system $(Q, \omega, H)$ from
the case $Q = T^*R^n$ to arbitrary symplectic manifolds. As it turns out, it is
precisely this index which appears as a Maslov phase in the trace formulas by
Gutzwiller and Duistermaat-Guillemin. Contribution presented at the XIX ICGTMP
Salamanca June 92.
