  We present the two-loop virtual QCD corrections to the scattering of massless
identical quarks, q qbar to q qbar, in conventional dimensional regularisation
and using the MSbar scheme. The structure of the infrared divergences agrees
with that predicted by Catani while expressions for the finite remainder are
given for the q qbar to qbar q and the q q to q q (qbar qbar to qbar qbar)
scattering processes in terms of polylogarithms. The results presented here
form a vital part of the next-to-next-to-leading order contribution to
inclusive jet production in hadron colliders and will play a crucial role in
improving the theoretical prediction for jet cross sections in hadron-hadron
collisions.
