A measurement of the inclusive semileptonic branching ratios of b hadrons produced in Z decay is presented, using four million hadronic events collected by the ALEPH detector from 1991 to 1995. Electrons and muons are selected opposite to b-tagged hemispheres. Two different methods are explored to distinguish the contributions from direct b → Xlν and cascade b → c → Xlν decays to the total lepton yield. One is based on the lepton transverse momentum spectrum, the other makes use of the correlation between the charge of the lepton and charge estimators built from tracks in the opposite hemisphere of the event. The latter method reduces the dependence on the modelling of semileptonic b decays. The results obtained by averaging the two techniques are BR(b → Xlν) = 0.1070 ± 0.0010stat± 0.0023syst± 0.0026model, BR(b → c → Xlν) = 0.0818 ± 0.0015stat± 0.0022syst-0.0014 model+0.0010. © Springer-Verlag / Società Italiana di Fisica 2001.