EN
Spin-polarized transport through a single-level quantum dot interacting with a local phonon mode is studied in the frame of the nonequilibrium Green-function technique. It is shown that strong electron-phonon interaction gives rise to a significant current suppression, to additional resonance peaks in the differential conductance as well as to oscillations of the tunnel magnetoresistance. Also, a phonon-induced mechanism leading to a minimum in tunnel magnetoresistance at zero bias voltage is explained.