  The cross sections for the reactions of muonium(anti-muonium) production in
high energy electron(positron) scattering by nuclei e^-(e^+) + Z -> Z +
M^0(anti-M^0) + mu^-(mu^+) are calculated in dependence on an energy and
polarization of an initial electron(positron) and a polarization of a final
mu^-(mu^+)-meson. Due to coherent phenomenon the cross sections are
proportional to Z^2. For Z ~ 100 due to the factor Z^2 the cross sections are
large enough to be measured at energies available at the HERA Collider in DESY.
The results are discussed in connection with a test of CPT invariance.
