We establish the general off-shell structure of the three neutral gauge bos
on self-couplings V-1*V-2*V-3*, 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 fermi
onic triangle loop. It covers both the standard model (SM) and possible new
physics (NP) contributions such as those arising in the minimal supersymme
tric SM. For what concerns NP contributions with a high scale, we discuss t
he validity of an effective Lagrangian involving a limited set of parameter
s. Finally we write the general expression of the V-1*V-2*V-3*-vertex contr
ibution to the e(+)e(-) --> (f (f) over bar) + (f'(f) over bar') amplitude.