  We list all the lowest dimension effective operators inducing off-shell
trilinear neutral gauge boson couplings Z-Z-Photon, Z-Photon-Photon, and ZZZ
within the effective Lagrangian approach, both in the linear and nonlinear
realizations of the SU(2)_{L} X U(1)_Y gauge symmetry. In the linear scenario
we find that these couplings can be generated only by dimension eight operators
necessarily including the Higgs boson field, whereas in the nonlinear case they
are induced by dimension six operators. We consider the impact of these
couplings on some precision measurements such as the magnetic and electric
dipole moments of fermions, as well as the Z boson rare decay Z ->
neutrino+antineutrino+ photon. If the underlying new physics is of a decoupling
nature, it is not expected that trilinear neutral gauge boson couplings may
affect considerably any of these observables. On the contrary, it is just in
the nonlinear scenario where these couplings have the more promising prospects
of being perceptible through high precision experiments.
