  We present the two-loop helicity amplitudes for the scattering of massless
quarks and massless gauge bosons in QCD. We use projector techniques to compute
the coefficients of the general tensor describing the two-quark two-boson
amplitude in conventional dimensional regularisation and use these coefficients
to derive the helicity amplitudes in the 't Hooft-Veltman scheme. The structure
of the infrared divergences agrees with that predicted by Catani while
expressions for the finite remainders for q qbar -> gluon gluon, q qbar ->
gluon gamma, q qbar -> gamma gamma and the processes related by crossing
symmetry are given in terms of logarithms and polylogarithms that are real in
the physical region. We have checked that the interference of tree and two-loop
helicity amplitudes, summed over helicities and colours, reproduces the
previous results for the finite remainders for interference of tree and
two-loop amplitudes given in Refs. [1,2]. We also find agreement with the
two-loop helicity amplitudes for quark-gluon scattering presented in Ref. [3].
