A search for the lepton flavour violating processes ep→μX and ep→τX is performed with the H1 experiment at HERA. Final states with a muon or tau and a hadronic jet are searched for in a data sample corresponding to an integrated luminosity of 66.5 pb-1 for e+p collisions and 13.7 pb-1 for e-p collisions at a centre-of-mass energy of 319 GeV. No evidence for lepton flavour violation is found. Limits are derived on the mass and the couplings of leptoquarks inducing lepton flavour violation in an extension of the Buchmüller–Rückl–Wyler effective model. Leptoquarks produced in ep collisions with a coupling strength of λ=0.3 and decaying with the same coupling strength to a muon–quark pair or a tau–quark pair are excluded at 95% confidence level up to masses of 459 GeV and 379 GeV, respectively.