Abstract submitted to the XXXth International Conference on High Energy Physics July 27 - August 2, 2000, Osaka, Japan _________________________________________________________________________ Search for lepton-flavour violation in ep collisions at HERA ZEUS Collaboration Abstract Events of the type e^+p -> l X, where l is a final-state higher-generation lepton (\mu or \tau) of high transverse momentum, have been sought at a centre-of-mass energy of 300 GeV with the ZEUS detector at HERA using an integrated luminosity of 47.7 pb^-1. No evidence was found for lepton-flavour violation. Constraints are set on the couplings of leptoquarks (LQs) mediating lepton-flavour-violating ep reactions. Limits are provided for the \tau decay channel for LQ masses below sqrt(s) and for both the \mu and \tau channels for LQ masses much greater than sqrt(s).