  Based on a recent proposal to build an electron-muon collider, we study
two-to-two production processes e^- mu^+ --> f bar-f, gamma gamma that
originate from dimension 6 and 8 operators. We compare the sensitivity to those
effective couplings obtained at the collider with that of low energy
measurements of mu --> e gamma, mu --> e bar-e e and mu --> e conversion that
have recently been reported in the literature. Whereas for the production of
first family fermions the sensitivity of the collider processes is much weaker,
for the second and third family fermions it is similar or stronger than that of
low-energy processes. In the case of e^- mu^+ --> gamma gamma, the sensitivity
to a dimension 8 contact operator turns out to be the strongest in comparison.
