Collins and Sivers asymmetries on the deuteron from the COMPASS data

COMPASS is a fixed target experiment presently running at CERN. In 2002, 2003, and 2004 it used a 160 GeV polarized muon beam coming from SPS and scattered off a $^{6}$LiD (deuteron) target. The nucleons in the target can be polarized either longitudinally or transversely with respect to the muon beam and 20% of the running time has been devoted to transverse polarization. Hereby the final results for the Collins and the Sivers asymmetries calculated from the data taken in transverse polarization in 2002 are presented. In the forthcoming 2006 run, COMPASS plans to run with a NH$_{3}$ (proton) target. Projections for the statistical accuracy which will be ultimately achieved on both the proton and the deuteron asymmetries are also given.