  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 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
approxmation, 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 H, Xe$^{53+}$, and
U$^{91+}$ (hydrogen-like) ions.
