Cross sections for the production of two isolated muons up to high di-muon masses are measured in ep collisions at HERA with the H1 detector in a data sample corresponding to an integrated luminosity of 71 pb−1 at a centre of mass energy of GeV. The results are in good agreement with Standard Model predictions, the dominant process being photon–photon interactions. Additional muons or electrons are searched for in events with two high transverse momentum muons using the full data sample corresponding to 114 pb−1, where data at GeV and GeV are combined. Both the di-lepton sample and the tri-lepton sample agree well with the predictions.