We consider a hyperbolic surface coming from a Fuchsian group without torsion. The topology of horocycles on such surfaces is completely described in the convex cocompact case : horocycles are either dense in the non-wandering set or closed topologically. But in the general case, the situation is different and the closure of a horycle may be more complex. Using the injectivity radius along a geodesic ray, we will explain the different types of closures of horocyclic orbits in the general case.