We perform a model-independent analysis so as to constrain the leptoquark (LQ) models from negative searches for mu-->e gamma, mu-->3e decays (and analogous processes in the tau sector), and coherent mu-e conversion in nuclei. We considerably improve some constraints obtained by analyses known in the literature, analyses which we show have by far underestimated the LQ contributions to the mu-->3e. In particular we find that the coherent mu-e conversion in nuclei mediated by the photon-conversion mechanism and the mu-->3e decay are golden plates where the flavor-changing leptoquark couplings, involving the second and third quark generations, can be strongly constrained. This is due to the fact that these processes Set the enhancements by large log(m(q)(2)/m(LQ)(2)) terms which are induced by the so-called "photon-penguin" diagrams. These enhancements, which produce a mild Glashow-Iliopoulos-Maiani (GIM) suppression in the amplitudes, have not been taken into account in the previous analyses. We show that the mu-->e gamma decay can set weaker constraints on the LQ models and this is because its amplitude is strongly GIM suppressed by the terms of order O(m(q)(2)/m(LQ)(2)). We also present the results for the corresponding constraints in the tau sector. Finally, the prospects of the future muon experiments for the improvement of the present bounds are analyzed and discussed.
