$e N \to \tau X$[@mutauDIS] by using the electron (positron) beam of a LC would be useful to further explore the tau lepton associated LFV Yukawa couplings.

In this talk, we discuss LFV in Higgs boson decays into a $\tau$-$\ell_i$ pair in the general framework of the THDM[@kot]. We study experimental upper limits on the tau lepton associated LFV Yukawa couplings to evaluate possible maximal values of the branching fractions. The parameter space of the model is tested by theoretical requirements for vacuum stability[@VS] and perturbative unitarity[@PU-1; @PU-2]. Current data from electroweak precision measurements at LEP[@LEP; @smlike1] and those at the B factories[@bsg-ex] also strongly constrain parameters of the Higgs potential. Under these theoretical bounds and experimental limits on the model, possible maximal values of the LFV couplings of $\tau$-$\ell_i$-$\phi^{0}$ are obtained by using the current data for rare tau decays, where $\phi^{0}$ represents two CP-even ($h$ and $H$) and a CP-odd ($A$) Higgs bosons. We then evaluate branching ratios of $\phi^0 \to \tau^\pm \ell_i^\mp$ with the maximal allowed values of the LFV couplings of $\tau$-$\ell_i$-$\phi^{0}$ in a wide range of the parameter space.

Lepton flavor violation in Yukawa interaction {#Sec:Model}
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The Higgs sector of the general THDM is 