  We consider in this Note resonances for a $h$-Pseudo-Differential Operator
$H(x,hD_x;h)$ on $L^2(M)$ induced by a periodic orbit of hyperbolic type, as
arises for Schr\"odinger operator with AC Stark effect when $M={\bf R}^n$, or
the geodesic flow on an axially symmetric manifold $M$, extending Poincar\'e
example of Lagrangian systems with 2 degrees of freedom. We generalize the
framework of [G\'eSj], in the sense that we allow for hyperbolic and elliptic
eigenvalues of Poincar\'e map, and look for so-called semi-excited resonances
with imaginary part of magnitude $-h\log h$, or $h^s$, with $0<s<1$.
