We study lepton flavour violating signals at a future e+e− linear collider within the general MSSM, allowing for the most general flavour structure. We demonstrate that there is a large region in parameter space with large signals, while being consistent with present experimental bounds on rare lepton decays such as μ− → e−γ. In our analysis, we include all possible signals from charged slepton, sneutrino, neutralino, and chargino production and decay. We also consider the background from the Standard Model and the MSSM. We find that in general the signature eτET / is the most pronounced one.