Abstract We investigate in detail the question of lepton-flavour violation in a SU(2) × U(1) supersymmetric model, where the breaking of supersymmetry (SUSY) is achieved through the coupling to N = 1 supergravity. It is shown that in the limit of degenerate neutrino masses, lepton flavour is exactly conserved. Allowing for neutrino masses compatible with present experimental limits, we analyse SUSY contributions to several lepton-flavour violating processes, comparing the size of these contributions with those already present in the standard Glashow-Salam-Weinberg model. In the case of μ → eγ, SUSY leads to a branching ratio two or three orders of magnitude larger than the corresponding branching ratio in the standard model, for gravitino and photino masses compatible with the experimental limits on the muon anomalous magnetic moment. In contrast, SUSY contributions to K L → μ e are always small, of the order of 10−2 of the corresponding amplitudes in the standard model, if the gravitino and photino masses are constrained by the KL − KS mass difference.