  A singular foliation on a complete riemannian manifold M is said to be
riemannian if each geodesic that is perpendicular at one point to a leaf
remains perpendicular to every leaf it meets. We prove that the regular leaves
are equifocal, i.e., the end point map of a normal foliated vector field has
constant rank. This implies that we can reconstruct the singular foliation by
taking all parallel submanifolds of a regular leaf with trivial holonomy. In
addition, the end point map of a normal foliated vector field on a leaf with
trivial holonomy is a covering map. These results generalize previous results
of the authors on singular riemannian foliations with sections.
