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We evaluate the lepton flavour violating (LFV) decays of HIggs bosonsH->li+lj in several extensions of the SM, including both the effectivelagrangian approach and several specific models. For the effective lagrangiancase, we focus on dimension-six operators that induce LFV vertices for theHiggs and or Z bosons. For those operators whose coefficients can not beconstrained by present data, LFV Higgs decays can have a B.R. of order0.1-0.01. Those cases when current bounds apply, induce strong bounds for e-mutransitions, and the b.r. for H->e mu is of order 10^-9; however H->tau mu, taue, can have B.R. of order 0.1. In the case of the two-higgs doublet model III,we obtain a similar B.R. for H-> tau mu, tau e, whereas in the SM with massiveneutrinos and the minimal SUSY-SM the corresponding B.R. are very suppressed.Comment: 15 pages, 3 figures, 2 table

Lepton flavor violating decays of Higgs bosons beyond the standard model