  We study the attractor mechanism for N=1 supergravity coupled to vector and
chiral multiplets and compute the attractor equations of these theories. These
equations may have solutions depending on the choice of the holomorphic
symmetric matrix f_{\Lambda\Sigma} which appears in the kinetic lagrangian of
the vector sector. Models with non trivial electric-magnetic duality group
which have or have not attractor behavior are exhibited. For a particular class
of models, based on an N=1 reduction of homogeneous special geometries, the
attractor equations are related to the theory of pure spinors.
