  A nonlocal gravity model, which does not assume the existence of a new
dimensional parameter in the action and includes a function $f(\Box^{-1} R)$,
with $\Box$ the d'Alembertian operator, is considered. The model is proven to
have de Sitter solutions only if the function f satisfies a certain
second-order linear differential equation. The de Sitter solutions
corresponding to the simplest case, an exponential function f, are explored,
without any restrictions on the parameters. If the value of the Hubble
parameter is positive, the de Sitter solution is stable at late times, both for
negative and for positive values of the cosmological constant. Also, the
stability of the solutions with zero cosmological constant is discussed and
sufficient conditions for it are established in this case. New de Sitter
solutions are obtained which correspond to the model with dark matter and
stability is proven in this situation for nonzero values of the cosmological
constant.
