  The analytic continuation of the Mellin transforms to complex values of N for
the basic functions $g_i(x)$ of the momentum fraction x emerging in the
quantities of massless QED and QCD up to two-loop order, as the unpolarized and
polarized splitting functions, coefficient functions, and hard scattering cross
sections for space- and time-like momentum transfer are evaluated. These Mellin
transforms provide the analytic continuations of all finite harmonic sums up to
the level of the threefold sums of transcendentality four, where the basis-set
${g_i(x)}$ consists of products of {\sc Nielsen}-integrals up to
transcendentality four. The computer code {\tt ANCONT} is provided.
