  The Super-Kamiokande atmospheric neutrino data suggest existence of the large
lepton-flavor violating (LFV) interaction in the higher energy scale. If the
minimal supersymmetric standard model is extended to have right-handed
neutrinos, the left-handed sleptons in the second and third generations are
expected to have the LFV masses in the minimal supergravity scenario. In this
article we study the LFV signals in the left-handed slepton production at
$\mu^+\mu^-$ colliders and $\e^+\e^-$ linear colliders (LC's),
$\mu^+\mu^-(\e^+\e^-)\to\tau\mu +4jets + \E$ and
$\mu^+\mu^-(\e^+\e^-)\to\tau\mu l+ 2jets+ \E$. The main background comes from
decay of a tau lepton into a muon in the lepton-flavor conserving slepton pair
production. They are significantly reduced by the energy and the impact
parameter cuts for the muon. At $\mu^+\mu^-$ colliders (LC's) it may be
possible to reach the mixing angle $\sin 2\theta_{\tilde{\nu}} \gsim 0.1(0.5)$
and the mass difference $\Delta m_{\tilde{\nu}}\gsim 0.1(0.4)$ GeV for the
sneutrinos in the second and third generations at the statistical significance
of $3\sigma$. Such small mass difference and a mixing angle may be induced
radiatively even if the Yukawa coupling constant for the tau neutrino is of the
order of 0.1.
