  We present the two-loop helicity amplitudes for the scattering of massless
quarks in QCD. We use projector techniques to compute the coefficients of the
general four-quark amplitude at up to two-loops 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
$q \bar q \to Q\bar Q$ 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].
