  Multi-electron production is studied at high electron transverse momentum in
positron- and electron-proton collisions using the H1 detector at HERA. The
data correspond to an integrated luminosity of 115 pb-1. Di-electron and
tri-electron event yields are measured. Cross sections are derived in a
restricted phase space region dominated by photon-photon collisions. In general
good agreement is found with the Standard Model predictions. However, for
electron pair invariant masses above 100 GeV, three di-electron events and
three tri-electron events are observed, compared to Standard Model expectations
of 0.30 \pm 0.04 and 0.23 \pm 0.04, respectively.
