We present a new measurement of the longitudinal spin asymmetry A1
and the spin-dependent structure function g1 of the deuteron in the range 1<Q2 < 100 GeV2 and 0.004 < x < 0.7. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarised muon beam and a large polarised 6LiD target. The results are in agreement with those from
previous experiments and improve considerably the statistical accuracy in the region 0.004<x <0.03.
