We consider a class of models predicting new heavy neutral fermionic s
tates, whose mixing with the light neutrinos can be naturally signific
ant and produce observable effects below the threshold for their produ
ction. We update the indirect limits on the flavour non-diagonal mixin
g parameters that can be derived from unitarity, and show that signifi
cant rates are in general expected for one-loop-induced rare processes
due to the exchange of virtual heavy neutrinos, involving the violati
on of the muon and electron lepton numbers. In particular, the amplitu
des for mu-e conversion in nuclei and for mu --> ee(+)e(-) show a non-
decoupling quadratic dependence on the heavy neutrino mass M, while mu
--> e gamma is almost independent of the heavy scale above the electr
oweak scale. These three processes are then used to set stringent cons
traints on the flavour-violating mixing angles. In all the cases consi
dered, we point out explicitly that the non-decoupling behaviour is st
rictly related to the spontaneous breaking of the SU(2) symmetry.