  We present the two-loop corrected operator matrix elements calculated in
N-dimensional regularization up to the finite terms which survive in the limit
$\epsilon = N - 4 \to 0 $. The anomalous dimensions of the local operators have
been previously extracted from the pole terms and determine the scale evolution
of the deep inelastic structure functions measured in unpolarized lepton hadron
scattering. The finite $\epsilon$-independent terms in the two-loop expressions
are needed to renormalize the local operators up to third order in the strong
coupling constant $\alpha_s$. Further the unrenormalized expressions for the
two-loop corrected operator matrix elements can be inserted into specific one
loop graphs to obtain a part of the third order contributions to these matrix
elements. This work is a first step in obtaining the anomalous dimensions up to
third order so that a complete next-to-next-to-leading order (NNLO) analysis
can be carried out for deep inelastic electroproduction.
