  We present the analytic next-to-next-to-leading QCD calculation of some
higher moments of deep inelastic structure functions in the leading twist
approximation. We give results for the moments $N$=1,3,5,7,9,11,13 of the
structure function $F_3$. Similarly we present the moments $N$=10,12 for the
flavour singlet and $N$=12,14 for the non-singlet structure functions $F_2$ and
$F_L$. We have calculated both the three-loop anomalous dimensions of the
corresponding operators and the three-loop coefficient functions of the moments
of these structure functions.
