Poincare series of geometrically finite groups

In this paper, we study the behaviour of the Poincare series of a geometric ally finite group Gamma of isometries of a riemannian manifold X with pinch ed curvature, in the case when Gamma contains parabolic elements. We give a sufficient condition on the parabolic subgroups of Gamma in order that Gam ma be of divergent type. When Gamma is of divergent type, we show that the Sullivan measure on the unit tangent bundle of X/Gamma is finite if and onl y if certain series which involve only parabolic elements of Gamma are conv ergent. We build also examples of manifolds X on which geometrically finite groups of convergent type act.