  Two-loop corrections for the <VVA> correlator of the singlet axial and vector
currents in QCD are calculated in the chiral limit for arbitrary momenta.
Explicit calculations confirm the non-renormalization theorems derived recently
by Vainshtein and Knecht et.al. We find that as in the one-loop case also at
the two loops the <VVA> correlator has only 3 independent form-factors instead
of 4. From the explicit results we observe that the two-loop correction to the
correlator is equal to the one-loop result times the constant factor C_2(R)
alpha_s/pi in the MSbar scheme. This holds for the full correlator, for the
anomalous longitudinal as well as for the non- anomalous thansversal
amplitudes. The finite overall alpha_s dependent constant has to be normalized
away by renormalizing the axial current according to Witten's
algebraic/geometrical constraint on the anomalous Ward identity. Our
observations, together with known facts, suggest that in perturbation theory
the <VVA> correlator is proportional to the one-loop term to all orders and
that the non- renormalization theorem of the Adler-Bell-Jackiw anomaly carries
over to the full correlator.
