We show theoretically that the longitudinal-transverse splitting of exciton-polaritons in semiconductor microcavities induces precession of polariton pseudospins. This precession manifests itself in pronounced oscillations of the polarization degree of time-resolved photoluminescence of microcavities. This effect combined with spin-dependent stimulated scattering of exciton-polaritons is responsible for the unusual polarization dynamics of emission of microcavities, recently reported [M. D. Martin et al., Phys. Rev. Lett 89, 077402 (2002)].