Résumé
On geometrically finite negatively curved surfaces, we give necessary and sufficient conditions for a one-sided horocycle (h(s)u)(s)>= 0 to be dense in the nonwandering set of the horocyclic flow. We prove that all dense one-sided orbits (h(s)u)(s)>= 0 are equidistributed, extending results of Burger ['Horocycle flows on geometrically finite surfaces', Duke Math. J. 61 (1990) 779-803] and Schapira ['Equidistribution of the horocycles of a geometrically finite surface', Int. Math. Res. Not. 40 (2005) 2447-2471] where symmetric horocycles (h(s)u)-R <=(s)<= R were considered.