  We prove a set of identities for the anomalous dimensions of the quark and
gluon conformal operators in the flavour singlet channel in QCD. These
relations arise from the graded commutator algebra of the N=1 superconformal
group. We evaluate the rotation matrices for the quantities under study from
the conventional dimensional regularization to the supersymmetry preserving
regularization scheme. Using them we verify the equalities in two-loop
approximation employing the results for the NLO anomalous dimensions of the
conformal operators in the minimal subtraction scheme derived earlier.
