  We study the geodesic flow on the unit tangent bundle of a rank one manifold
and we give conditions under which all classical definitions of pressure of a
H\"older continuous potential coincide. We provide a large deviation statement,
which allows to neglect (periodic) orbits that lack sufficient hyperbolic
behavior. Our results involve conditions on the potential, that take into
consideration its properties in the nonhyperbolic part of the manifold. We draw
some conclusions for the construction of equilibrium states.
