  With $\mu\to e\gamma$ decay forbidden by multiplicative lepton number
conservation, we study muonium--antimuonium transitions induced by neutral
scalar bosons. Pseudoscalars do not induce conversion for triplet muonium,
while for singlet muonium, pseudoscalar and scalar contributions add
constructively. This is in contrast to the usual case of doubly charged scalar
exchange, where the conversion rate is the same for both singlet and triplet
muonium. Complementary to muonium conversion studies, high energy $\mu^+e^- \to
\mu^- e^+$ and $e^-e^- \to \mu^- \mu^-$ collisions could reveal spectacular
resonance peaks for the cases of neutral and doubly charged scalars,
respectively.
