  We study a generalized Einstein theory with the following two criteria:{\it
i}) on the solar scale, it must be consistent with the classical tests of
general relativity, {\it ii}) on the galactic scale, the gravitational
potential is a sum of Newtonian and Yukawa potentials so that it may explain
the flat rotation curves of spiral galaxies. Under these criteria, we find that
such a generalized Einstein action must include at least one scalar field and
one vector field as well as the quadratic term of the scalar curvature.
