  Processes leading to a final state with at least two high transverse momentum
leptons (electrons or muons) are studied using the full ep data sample
collected by the H1 experiment at HERA. The data correspond to an integrated
luminosity of 463 pb-1. Di-lepton and tri-lepton event classes are
investigated. Cross sections of the production of e+e- and mu+mu- pairs are
derived in a restricted phase space dominated by photon-photon collisions. In
general, good agreement is found with Standard Model predictions. Events are
observed with a total scalar sum of lepton transverse momenta above 100 GeV
where the Standard Model expectation is low. In this region, combining
di-lepton and tri-lepton classes, five events are observed in e+p collisions,
compared to a Standard Model expectation of 0.96+-0.12, while no such event is
observed in e-p data for 0.64+-0.09 expected.
