  In the years 2002-2004 COMPASS has collected data with the LiD target
polarization oriented transversely with respect to the muon beam direction for
about 20% of the running time, to measure transverse spin effects in
semi-inclusive deep inelastic scattering, one of the main objectives of the
COMPASS spin program. In 2007, COMPASS has used for the first time a proton
NH_3 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.
