We report on a search for the lepton-flavor-violating processes e+e-→μ+τ- and e+e-→e+τ-. The data sample corresponds to an integrated luminosity of 211fb-1 recorded by the BABAR experiment at the SLAC PEP-II asymmetric-energy B Factory at a center-of-mass energy of s=10.58GeV. We find no evidence for a signal and set the 90% confidence level upper limits on the cross sections to be σμτ<3.8fb and σeτ<9.2fb. The ratio of the cross sections with respect to the dimuon cross section are measured to be σμτ/σμμ<3.4×10-6 and σeτ/σμμ<8.2×10-6. © 2007 The American Physical Society.