  On the unit tangent bundle of a nonflat compact nonpositively curved surface,
we prove that there is a unique probability Borel measure invariant by a
horocyclic flow which gives full measure to the set of rank $1$ vectors
recurrent by the geodesic flow. If we assume in addition that the surface has
no flat strips, we show that the horocyclic flow is uniquely ergodic. These
results are valid for any parametrization of the horocyclic flow.
