The radiative mass structure of some Grand Unified Models is discussed. They contain fermions with SU(2)-invariant masses in the desert. The possibility of such fermions is examined in detail with the conclusion that their mass can be low enough (~ 20 GeV) to be found in accelerators today. The mixing of such fermions with ordinary fermions is analysed and their contribution to rare processes calculated. They do not upset standard GUT predictions. Finally an analysis of their contribution to the μ → eγ rate is an interesting illustration of decoupling.