  We discuss the cosmological implications of the $R~\Box^{-2}R$ nonlocal
modification to standard gravity. We relax the assumption of special initial
conditions in the local formulation of the theory, perform a full phase-space
analysis of the system, and show that the late-time cosmology of the model
exhibits two distinct evolution paths, on which a large range of values for the
present equation of state can be reached. We then compare the general solutions
to supernovae data and place constraints on the parameters of the model. In
particular, we find that the mass parameter of the theory should be smaller
than 1.2 in Hubble units.
