  We establish the general off-shell structure of the three neutral gauge boson
self-couplings V1*V2*V3*, with applications to the Z*Z*Z*, Z*Z*gamma*,
gamma*gamma*Z* cases. New coupling forms appear which do not exist when two
gauge bosons are on-shell. We give the contribution arising from a fermionic
triangle loop. It covers both the standard model (SM) and possible new physics
(NP) contributions like those arising in the MSSM. For what concerns NP
contributions with a high scale, we discuss the validity of an effective
Lagrangian involving a limited set of parameters. Finally we write the general
expression of the V1*V2*V3*-vertex contribution to the e+e- to (f(bar)
f)+(f'(bar) f') amplitude.
