  We present an analytic expression for the two-loop QCD corrections to the
decay process b -> u W^*, where b and u are a massive and massless quark,
respectively, while W^* is an off-shell charged weak boson. Since the W-boson
can subsequently decay in a lepton anti-neutrino pair, the results of this
paper are a first step towards a fully analytic computation of differential
distributions for the semileptonic decay of a b-quark. The latter partonic
process plays a crucial role in the study of inclusive semileptonic charmless
decays of B-mesons. The three independent form factors characterizing the b W u
vertex are provided in form of a Laurent series in (d-4), where d is the
space-time dimension. The coefficients in the series are expressed in terms of
Harmonic Polylogarithms of maximal weight 4, and are functions of the invariant
mass of the leptonic decay products of the W-boson.
