We have searched for the lepton-flavor-violating decays tau- -> ell-K0s and ell-K0sK0s (ell = e or mu), using a data sample of 671 fb^-1 collected with the Belle detector at the KEKB asymmetric-energy e^+e^- collider. No evidence for a signal was found in any of the decay modes, and we set the following upper limits for the branching fractions: B(tau^- -> e^-K0s) < 2.6 x 10^-8, B(tau^- -> mu^-K0s) < 2.3 x 10^-8, B(tau^- -> e^-K0sK0s) < 7.1 x 10^-8 and B(tau^- -> mu^-K0sK0s) < 8.0 x 10^-8 at the 90% confidence level.
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