  In this paper we study the equilibrium configurations of anisotropic
self-gravitating fermions, by extending to general relativity the solutions
obtained in a previous paper. This treatment also generalizes to anisotropic
systems the relativistic self-gravitating Fermi gas model, by considering
different degrees of anisotropy. We discuss some important characteristics of
the models and the obtained density profiles, and generalize the relation
between the anisotropy and the mass of particles in the relativistic regime.
These relativistic models may also be applied to the study of superdense
neutron stars with anisotropic pressure or super-Chandrasekhar white dwarfs
generated by the presence of a magnetic field.
