  We present an algorithm for the analytical evaluation of dimensionally
regularized massless on-shell double box Feynman diagrams with arbitrary
polynomials in numerators and general integer powers of propagators. Recurrence
relations following from integration by parts are solved explicitly and any
given double box diagram is expressed as a linear combination of two master
double boxes and a family of simpler diagrams. The first master double box
corresponds to all powers of the propagators equal to one and no numerators,
and the second master double box differs from the first one by the second power
of the middle propagator. By use of differential relations, the second master
double box is expressed through the first one up to a similar linear
combination of simpler double boxes so that the analytical evaluation of the
first master double box provides explicit analytical results, in terms of
polylogarithms $\Li{a}{-t/s}$, up to $a=4$, and generalized polylogarithms
$S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables
$s$ and $t$, for an arbitrary diagram under consideration.
