A general analysis of the lowest-dimensional P-odd Z gamma gamma gamma
interaction is performed. It turns out that there are only two indepe
ndent gauge invariant dimension-eight effective Lagrangians of such a
type, similarly to the P-even case discussed earlier. It is shown, tha
t such an effective interaction is naturally induced, at the two-loop
level, within an extension of the standard model of electroweak intera
ctions involving two-doublet CP-violating Higgs sector.