  On geometrically finite negatively curved surfaces, we give necessary and
sufficient conditions for a one-sided horocycle $(h^s u)_{s\ge 0}$ to be dense
in the nonwandering set of the geodesic flow. We prove that all dense one-sided
orbits $(h^su)_{s\ge 0}$ are equidistributed, extending results of [Bu] and
[Scha2] where symmetric horocycles $(h^su)_{s\in\R}$ were considered.
