  The field equations of the recent nonlocal generalization of Einstein's
theory of gravitation are presented in a form that is reminiscent of general
relativity. The implications of the nonlocal field equations are studied in the
case of conformally flat spacetimes. Even in this simple case, the field
equations are intractable. Therefore, to gain insight into the nature of these
equations, we investigate the structure of nonlocal gravity in two-dimensional
spacetimes. While any smooth 2D spacetime is conformally flat and satisfies
Einstein's field equations, only a subset containing either a Killing vector or
a homothetic Killing vector can satisfy the field equations of nonlocal
gravity.
