A search has been performed for the decays μ → eee, μ → e γ, and μ → eγγ with a sensitivity in the branching ratios at the level of 10 −10. The experiment used a separated, 26 MeV/c μ + beam with an average intensity of 300kHz. A total of 2.2 × 10 11 muon decays were examined for the present result. The detector for the experiment Is the Crystal Box, which consists of a cylindrical drift chamber surrounded by 396 NaI(T1) crystals. A layer of scintillation counters in front of the crystals provided timing for electrons and a veto for photons. The energy resolution for electrons and photons is ≈6% (FWHM). The position resolution of the drift chamber is 350 μm leading to a vertex cut with a rejection of 10 3 for μ → eee. The timing resolution is ≈300 ps from the scintillators and ~1 ns from the crystals. No candidate for μ → eee has been found, yielding an upper limit for the branching ratio of B μ3e < 1.3 × 10 −10 (90% C.L.).