  Dimuonium (the bound system of two muons, $\mu^+\mu^-$-atom) has not been
observed yet. In this paper we discuss the electromagnetic production of
dimuonium at RHIC and LHC in relativistic heavy ion collisions. The production
of parastates is analyzed in the equivalent photon approximation. For the
treatment of orthostates, we develop a three photon formalism. We determine the
production rates at RHIC and LHC with an accuracy of a few percent and discuss
problems related to the observation of dimuonium.
