  A new representation is found for the action of the recently suggested
ghost-free nonlocal gravity models generating de Sitter or Anti-de Sitter
background with an arbitrary value of the effective cosmological constant. This
representation allows one to extend applications of these models from maximally
symmetric to generic Einstein spaces and black hole solutions, but clearly
indicates violation of the general relativistic limit in this class of
theories, induced by their infrared behavior. It is shown that this limit can
be recovered in a special conformal frame of these theories, and their relation
to critical gravity models is also briefly discussed.
