  We study the closure of horocycles on rank 1 nonpositively curved surfaces
with finitely generated fundamental group. Each horocycle is closed or dense on
a certain subset of the unit tangent bundle. In fact, we classify each
half-horocycle in terms of the associated geodesic rays. We also determine the
nonwandering set of the horocyclic flow and characterize the surfaces admitting
a minimal set for this flow.
