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We report new measurements of semileptonic branching fractions of B mesons produced at the '(4S) resonance determined by fitting the inclusive electron and muon momentum spectra to different theoretical models. Using B(B»'X"-») to denote the average of the semileptonic branching fractions for B decay to electrons and muons, we obtain B(B»'X"-»)= (10.5±0.2±0.4)% using the refined free-quark model of Altarelli et al., and B(B»'X"-»)=(11.2±0.3±0.4)% using a modified version of the form-factor model of Isgur et al., in which the D**"-» contribution is allowed to float in the fit. The average of these two results is B(B»'X"-»)=(10.8±0. 2±0.4±0.4)%, where the errors are statistical, systematic uncertainties in the measurement, and systematic uncertainties associated with the theoretical models, respectively. Semileptonic branching fractions as low as this are difficult to accommodate in theoretical models where hadronic B-meson decays arise only from spectator diagrams. We use dilepton yields to limit the uncertainty in the semileptonic branching fraction due to the possible existence of non-BB» decays of the '(4S). In addition, we tag neutral B mesons using the decays B»0'D*+- and B»0'D*+"-» to obtain the first direct measurement of semileptonic branching fractions for neutral B mesons; the average of the electron and muon results for neutral B mesons is B(B»0'X"-»)=(9.9±3.0±0.9)%. © 1992 The American Physical Society.