  We describe the calculation of all planar master integrals that are needed
for the computation of NNLO QCD corrections to the production of two off-shell
vector bosons in hadron collisions. The most complicated representatives of
integrals in this class are the two-loop four-point functions where two
external lines are on the light-cone and two other external lines have
different invariant masses. We compute these and other relevant integrals
analytically using differential equations in external kinematic variables and
express our results in terms of Goncharov polylogarithms. The case of two equal
off-shellnesses, recently considered in Ref. [1], appears as a particular case
of our general solution.
