The inclusive semileptonic branching ratios b --> e nu X, mu nu X, tau nu X and nu X have been measured at LEP with the L3 detector. The analysis is based on 2-jet hadronic Z decays obtained in the data collected between 1991 and 1992. Three separate event samples are analysed, containing electrons, muons and large missing energy (neutrinos), respectively. From the electron sample, we measure Br(b --> e nu X) = (10.89+/-0.20+/-0.51)% and, from the muon sample, Br(b --> mu nu X) = (10.82+/-0.15+/-0.59)%, where the first error is statistical and the second is systematic. From the missing energy sample, we measure Br(b --> nu X) = (23.08+/-0.77+/-1.24)%, assuming the relative semileptonic decay rates e:mu:tau = 1:1:(0.25+/-0.05), according to theoretical expectations. From a combined analysis of all three samples and constraining the relative semileptonic rates, we measure Br(b --> e nu X) = Br(b --> mu nu X) = (10.68+/-0.11+/-0.46)%. Alternatively, we can remove the constraint on the relative semileptonic rates and measure Br(b --> tau nu X) = (1.7+/-0.5+/-1.1)%.