Accepted Tuesday Oct 13, 2009
We study a new supersymmetric mechanism for lepton flavour violation in m and t decays and m e conversion in nuclei, within a minimal extension of the MSSM with low-mass heavy singlet neutrinos and sneutrinos. We find that the decays meg, t eg and t mg are forbidden in the supersymmetric limit of the theory, whereas other processes, such as m eee, m e conversion, t eee and t emm, are allowed and can be dramatically enhanced several orders of magnitude above the observable level by potentially large neutrino Yukawa coupling effects. The profound implications of supersymmetric lepton flavour violation for present and future experiments are discussed.