  This paper deals with the production of orthodimuonium (OM) ($\mu^{+}
\mu^{-}$ atom in triplet state) in collisions of high-energy electrons with
nuclei or atoms. This reaction was previously studied by Holvik and Olsen
[Phys. Rev. D 35, 2124 (1987)] on the basis of a bremsstrahlung mechanism where
OM is produced by only one virtual photon. In the present paper we consider a
competing three-photon mechanism where the production of OM results from the
collision of a photon generated by the electron with two photons emitted by the
nucleus. We derive the corresponding spectrum and production rate of OM and
show that the three-photon mechanism is the dominant one for heavy atom target.
