  Present evidences for neutrino masses and lepton flavour mixings allow to
predict, in the Standard Model with light neutrinos, branching rates for the
decays Z --> e mu, mu tau, e tau of less than 10^{-54}, while present
experimental exclusion limits from LEP 1 are of order 10^{-5}. The GigaZ option
of the TESLA Linear Collider project will extend the sensitivity down to about
10^{-8}. We study in a systematic way some minimal extensions of the Standard
Model and show that GigaZ might well be sensitive to the rates predicted from
these scenarios.
