  Martinus Veltman was the first to point out the inconsistency of the
experimental value for the decay rate of $\pi^0\rightarrow\gamma\gamma$ and its
calculation by J. Steinberger with the very successful concept of the pion as
the (pseudo)Nambu-Goldstone boson of the spontaneously broken global axial
symmetry of strong interactions. That inconsistency has been resolved by J.
Bell and R. Jackiw in their famous paper on the chiral anomalies. We review the
connection between the decay amplitudes of an axion into two gauge bosons in
Abelian vector-like and chiral gauge theories. The axion is the Nambu-Goldstone
boson of a spontaneously broken axial global symmetry of the theory. Similarly
as for the vector-like gauge theory, also in the chiral one the axion decay
amplitude is determined by the anomaly of the current of the axial symmetry in
its non-linear realization. Certain subtlety in the calculation of the anomaly
in chiral gauge theories is emphasised.
