In the list of the main items studied by the CERN COMPASS experiment there are the transverse spin and momentum effects visible in the azimuthal distributions of hadrons produced in the deep inelastic scattering. In the years 2002-2004 COMPASS has collected data with a 6LiD target with the polarization oriented transversely with respect to the muon beam direction for about 20% of the running time; in 2007, COMPASS has used for the first time a proton NH3 target with the data taking time equally shared between longitudinal and transverse polarization of the target. After reviewing the results obtained with the deuteron, the new results for the Collins and Sivers asymmetries of the proton will be presented.
