  We investigate various perturbative properties of the deformed N=4 SYM
theory. We carry out a three-loops calculation of the chiral matter superfield
propagator and derive the condition on the couplings for maintaining finiteness
at this order. We compute the 2-, 3- and 4-point functions of composite
operators of dimension 2 at two loops. We identify all the scalar operators
(chiral and non-chiral) of bare dimension 4 with vanishing one-loop anomalous
dimension. We compute some 2- and 3-point functions of these operators at two
loops and argue that the observed finite corrections cannot be absorbed by a
finite renormalization of the operators.
