Let M be a manifold with pinched negative sectional curvature. We show that when M is geometrically finite and the geodesic flow on T 1 M is topologically mixing then the set of mixing invariant measures is dense in the set M 1 (T 1 M) of invariant probability measures. This implies that the set of weak-mixing measures which are invariant by the geodesic flow is a dense G δ subset of M 1 (T 1 M). We also show how to extend these results to manifolds with cusps or with constant negative curvature.