Analytic formulae are given for order alpha(s) perturbative QCD corrections to the double differential distribution of the tau lepton energy and the invariant mass of the tau + antineutrino system in semileptonic decays of the bottom quark. The corresponding distribution for B meson decays are obtained by combining these results and the non-perturbative QCD corrections calculated by Falk et al. The moments of the energy distribution of the tau lepton are calculated. (C) 1997 Elsevier Science B.V.