  We investigate the attractor mechanism for spherically symmetric extremal
black holes in a theory of general $R^2$ gravity in 4-dimensions, coupled to
gauge fields and moduli fields. For the general $R^2$ theory, we look for
solutions which are analytic near the horizon, show that they exist and enjoy
the attractor behavior. The attractor point is determined by extremization of
an effective potential at the horizon. This analysis includes the backreaction
and supports the validity of non-supersymmetric attractors in the presence of
higher derivative interactions. To include a wider class of solutions, we
continue our analysis for the specific case of a Gauss-Bonnet theory which is
non-topological, due to the coupling of Gauss-Bonnet terms to the moduli
fields. We find that the regularity of moduli fields at the horizon is
sufficient for attractor behavior. For the non-analytic sector, this regularity
condition in turns implies the minimality of the effective potential at the
attractor point.
