Our objective is to compute the moments of the deep-inelastic structur
e functions of the nucleon on the lattice. A major source of uncertain
ty is the renormalization of the lattice operators that enter the calc
ulation. In this talk we compare the renormalization constants of the
most relevant twist-two bilinear quark operators which we have compute
d non-perturbatively and perturbatively to one loop order. Furthermore
, we discuss the use of tadpole improved perturbation theory.