  We examine the Standard and the New Physics (NP) contributions to the ZZZ,
ZZgamma and Zgammagamma neutral gauge couplings. At the one-loop level, if we
assume that there is no CP violation contained in NP beyond the Standard Model
one, we find that only CP conserving neutral gauge couplings are generated,
either from the standard quarks and leptons, or from possible New Physics (NP)
fermions. Bosonic one-loop diagrams never contribute to these couplings, while
the aforementioned fermionic contributions satisfy hZ3=-fgamma5, hZ4=hgamma4=0.
We also study examples of two-loop NP effects that could generate non vanishing
h4 couplings. We compare quantitative estimates from SM, MSSM and some specific
examples of NP contributions, and we discuss their observability at future
colliders.
