  A general class of gravitational models driven by a nonlocal scalar field
with a linear or quadratic potential is considered. We study the action with an
arbitrary analytic function $F(\Box)$, which has both simple and double roots.
The way of localization of nonlocal Einstein equations is generalized on models
with linear potentials. Exact solutions in the Friedmann-Robertson-Walker and
Bianchi I metrics are presented.
