Search for New Physics in the Cosmic Rays with the Alpha Magnetic Spectrometer

The AMS measurements of the cosmic ray fluxes are revealing structures int the cosmic positron and electron energy spectra. Different interpretations on the origin of this spectral features have been advanced. One the of the most appealing is that they could originate from Dark Matter decay or annihilation. The most recent AMS results will be presented and the AMS capability in discriminating different models, by means of high statistic measurements of electron and positron fluxes will be discussed.