  The angular distribution of the emitted electrons, following the two--photon
ionization of the hydrogen--like ions, is studied within the framework of
second order perturbation theory \textit{and} the Dirac equation. Using a
density matrix approach, we have investigated the effects which arise from the
polarization of the incoming light as well as from the higher multipoles in the
expansion of the electron--photon interaction. For medium-- and high--Z ions,
in particular, the non--dipole contributions give rise to a significant change
in the angular distribution of the emitted electrons, if compared with the
electric--dipole approximation. This includes a strong forward emission while,
in dipole approximation, the electron emission always occurs symmetric with
respect to the plane which is perpendicular to the photon beam. Detailed
computations for the dependence of the photoelectron angular distributions on
the polarization of the incident light are carried out for the ionization of
the H, Xe$^{53+}$ and U$^{91+}$ (hydrogen--like) ions.
