  The possible form of New Physics (NP) interactions affecting the ZZZ, $ZZ
\gamma$ and $Z\gamma \gamma$ vertices, is critically examined. Their signatures
and the possibilities to study them, through ZZ and $Z\gamma$ production, at
the e^-e^+ Colliders LEP and LC and at the hadronic Colliders Tevatron and LHC,
are investigated. Experimental limits obtained or expected on each coupling are
collected. A simple theoretical model based on virtual effects due to some
heavy fermions is used for acquiring some guidance on the plausible forms of
these NP vertices. In such a case specific relations among the various neutral
couplings are predicted, which can be experimentally tested and possibly used
to constrain the form of the responsible NP structure.
