  We present the analytic calculation of the Mellin moments of the structure
functions F_2, F_3 and F_L in perturbative QCD up to second order corrections
and in leading twist approximation. We calculate the 2-loop contributions to
the anomalous dimensions of the singlet and non-singlet operator matrix
elements and the 2-loop coefficient functions of F_2, F_3 and F_L. We perform
the inverse Mellin transformation analytically and find our results in
agreement with earlier calculations in the literature by Zijlstra and van
Neerven.
