  The electron and muon number violating muonium-antimuonium oscillation
process can proceed provided neutrinos have non-zero masses and mix among the
various generations. Modifying the Standard Model only by the inclusion of
singlet right handed neutrino fields and allowing for general neutrino masses
and mixings, the leading order matrix element contributing to this process is
computed. For the particularly interesting case where the neutrino masses are
generated by a see-saw mechanism with a very large Majorana mass $M_R>>M_W$, it
is found that both the very light and very heavy Majorana neutrinos each give
comparable contributions to the oscillation time scale proportional to $M_R^2$.
Present experimental limits set by the non-observation of the oscillation
process sets a lower limit on $M_R$ of roughly of order $10^4$ GeV.
