  We present a theoretical model that allows us to describe the polariton
dynamics in a semiconductor microcavity at large densities, for the case of
non-resonant excitation. Exciton-polariton scattering from a thermalized
exciton reservoir is identified as the main mechanism for relaxation into the
lower polariton states. A maximum in the polariton distribution that shifts
towards lower energies with increasing pump-power or temperature is shown, in
agreement with recent experiments. Above a critical pump-power, macroscopic
occupancies (5 \times 10^4) can be achieved in the lowest energy polariton
state. Our model predicts the possibility of Bose-Einstein Condensation of
polaritons, driven by exciton-polariton interaction, at densities well below
the saturation density for CdTe microcavities.
