We present a measurement of the deuteron spin-dependent structure function
g1d based on the data collected by the COMPASS experiment at CERN during the
years 2002-2004. The data provide an accurate evaluation for Gamma_1^d, the
first moment of g1d(x), and for the matrix element of the singlet axial
current, a0. The results of QCD fits in the next to leading order (NLO) on all
g1 deep inelastic scattering data are also presented. They provide two
solutions with the gluon spin distribution function Delta G positive or
negative, which describe the data equally well. In both cases, at Q^2 = 3
(GeV/c)^2 the first moment of Delta G is found to be of the order of 0.2 - 0.3
in absolute value.Comment: fits redone using MRST2004 instead of MRSV1998 for G(x), correlation
matrix adde