We present a new measurement of the spin-dependent structure function g1d of the deuteron in deep inelastic scattering of 190 GeV polarised muons on polarised deuterons, in the kinematic range 0.003 <x <0.7 and 1 GeV2 <Q2 <60 GeV2. This structure function is found to be negative at small x. The first moment Γ1d=∫01g 1ddx evaluated at Q02 = 10 GeV2 is 0.034 ± 0.009 (stat.) ± 0.006 (syst.). This value is below the Ellis-Jaffe sum rule prediction by three standard deviations. Using our earlier determination of Γ1p, we obtain Γ1p - Γ1n = 0.199 ± 0.038 which agrees with the Bjorken sum rule. © 1995.