In section 1 we reformulate a theorem of Blichfeldt in the framework of
manifolds of nonpositive curvature. As a result we obtain a lower bound on the
number of homotopically distinct geodesic loops emanating from a common point q
whose length is smaller than a fixed constant. This bound depends only on the
volume growth of balls in the universal covering and the volume of the manifold
itself. We compare the result with known results about the asymptotic growth
rate of closed geodesics and loops in section 2.