  In this paper we have investigated the cosmological dynamics of non-locally
corrected gravity involving a function of the inverse d'Alembertian of the
Ricci scalar, $f(\Box^{-1} R))$. Casting the dynamical equations into local
form, we derive the fixed points of the dynamics and demonstrate the existence
and stability of a one parameter family of dark energy solutions for a simple
choice, $f(\Box^{-1} R)\sim \exp(\alpha \Box^{-1} R)$. The effective EoS
parameter is given by, $w_{\rm eff}=({\alpha-1})/({3\alpha-1})$ and the
stability of the solutions is guaranteed provided that $1/3<\alpha<2/3$. For
$1/3<\alpha<1/2$ and $1/2<\alpha<2/3$, the underlying system exhibits phantom
and non-phantom behavior respectively; the de Sitter solution corresponds to
$\alpha=1/2$. For a wide range of initial conditions, the system mimics dust
like behavior before reaching the stable fixed point. The late time phantom
phase is achieved without involving negative kinetic energy fields. A brief
discussion on the entropy of de Sitter space in non-local model is included.
