We analyze the available information on the interactions that can contribute to the decays η→π0μ±e, and discuss the implications for the η→π0μ±e branching ratios. For all cases the experimental results on μ-→e- conversion in nuclei set stringent limits on the strength of the interactions. For the case of a scalar interaction, which in renormalizable gauge theories is the only possible source of η→π0μ±e at the tree level, we find B(η→π0μ±e4×10-18. For interactions involving second-class currents the branching ratio is not likely to be larger than ∼10-15, which is still considerably below the level that could be explored at present. © 1995 The American Physical Society.