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.