  In semi-inclusive DIS of polarized leptons on a transversely polarized target
eight azimuthal modulations appear in the cross-section. Within QCD parton
model four azimuthal asymmetries can be interpreted at leading order, two of
them being the already measured Collins and Sivers asymmetries. The other two
leading twist asymmetries, related to different transverse momentum dependent
quark distribution functions, and also additional four asymmetries which can be
interpreted as twist-three contributions have been measured for the first time
at COMPASS, using a 160 GeV/c longitudinally polarized ($P_{beam}\simeq -0.8$)
muon beam and a transversely polarized $^6LiD$ target. We present here the
preliminary results from the 2002-2004 data.
