At variance with fully inclusive quantities, which have been computed
already at the two- or three-loop level, most exclusive observables are
still known only at one-loop, as further progress was hampered so far by
the greater computational problems encountered in the study of multi-leg
amplitudes beyond one loop. We show in this paper how the use of tools
already employed in inclusive calculations can be suitably extended to the
computation of loop integrals appearing in the virtual corrections to
exclusive observables, namely two-loop four-point functions with massless
propagators and up to one off-shell leg. We find that multi-leg
integrals, in addition to integration-by-parts identities, obey also
identities resulting from Lorentz-invariance. The combined set of these
identities can be used to reduce the large number of integrals appearing
in an actual calculation to a small number of master integrals. We then
write down explicitly the differential equations in the external
invariants fulfilled by these master integrals, and point out that the
equations can be used as an efficient method of evaluating the master
integrals themselves. We outline strategies for the solution of the
differential equations, and demonstrate the application of the method on
several examples.