COMPASS is a fixed-target experiment on the SPS M2 beamline at CERN. Its LiD target can be polarised both longitudinally and transversally with respect to the longitudinally polarised 160 GeV/c muon beam. Approximately 20% of the beam-time in 2002, 2003 and 2004 was spent in the transverse configuration, allowing the first measurement of both the Collins and Sivers asymmetries on a deuterium target. First results from the the transverse data of the COMPASS run in 2002 are reported here.