  The $e^+p$-data collected with the ZEUS (${\cal L}=47.7$ pb$^{-1}$) and the
H1 (${\cal L}=37$ pb$^{-1}$) detectors at HERA in 1994--1997 are analysed for
signals of lepton flavour violation mediated by leptoquark exchange, both in
the muon and the tau channels. No evidence for lepton flavour violation is
found and limits on the leptoquarks' Yukawa couplings are set.
