A phenomenological theory is given of possible "two-photon" neutrinoless muon → electron decay processes: ${\mu }^{\pm }\to e^{\pm }+\gamma +\gamma$; ${\mu }^{-}+\mathrm{nucleus}\to {\mu }^{-}+\gamma \left(\mathrm{virtual}\mathrm{Coulomb}\right)+\mathrm{nucleus}\to e^{-}+\gamma +\mathrm{nucleus}$; ${\mu }^{-}+\mathrm{nucleus}\to {\mu }^{-}+\gamma \left(\mathrm{virtual}\mathrm{Coulomb}\right)+\gamma \left(\mathrm{virtual}\mathrm{Coulomb}\right)+\mathrm{nucleus}\to e^{-}+\mathrm{nucleus}$. It is found that the decay, ${\mu }^{-}+\mathrm{nucleus}\to e^{-}+\gamma +\mathrm{nucleus}$, is the most probable of the three under consideration and a search for this as yet experimentally uninvestigated decay is suggested.

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