  In this thesis we discuss the decays of the pseudoscalar mesons (the neutral
pion, the eta and eta-prime) which are governed by the chiral anomaly. Some of
these decays are of special interest because their study permits a deep insight
into aspects of modern physics. The decays can be classified according to the
type of the anomaly (triangle or box) that governs the corresponding amplitude
when it is extrapolated to the chiral point. In order to take the momentum
dependencies of the form factors into account, the actual calculations are
performed in the frame work of vector meson dominance (VMD) models, namely in
terms of the original hidden gauge model and modern generalized models. The
results of the triangle-anomaly sector show that the hidden gauge model and the
modern modifications can describe the data equally well. In the box-anomaly
sector the data have a slight preference to the modern modified VMD
formulation. The results of the latter also agree very well with the
predictions of unitarized chiral perturbation theory. In the case of the
box-anomaly decays, we especially analyze the contributions of an
unconventional untested CP-violating electric dipole form factor that is
sensitive to the strange-quark/antiquark-content of the eta and eta-prime
mesons. We verify the claim that it could still be of natural size by comparing
with the new KLOE data for eta-> pi+ pi- e+ e-.
