  We discuss predictions for the lepton-flavour changing decays Z --> e mu, mu
tau, e tau which may be searched for at the Giga-Z option of the Tesla Linear
Collider project with Z resonance production rates as high as 10^9. We try to
be as model-independent as possible and consider both the Dirac and Majorana
mass cases. The Standard Model, if being minimally extended by the inclusion of
light neutrino masses with some mixings as observed in neutrino oscillation
search experiments, predicts completely negligible rates. With a more general
neutrino content quite interesting expectations may be derived.
