  A nonlocal gravity model with a function $f(\Box^{-1} R)$, where $\Box$ is
the d'Alembert operator, is considered. The algorithm, allowing to reconstruct
$f(\Box^{-1} R)$, corresponding to the given Hubble parameter and the state
parameter of the matter, is proposed. Using this algorithm, we find the
functions $f(\Box^{-1} R)$, corresponding to de Sitter solutions.
