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We report on a search for the lepton-flavor-violating processes
$e^+e^- \rightarrow \mu^+\tau^-$ and $e^+e^- \rightarrow e^+\tau^-$.
The data sample corresponds to an integrated luminosity of 211
fb$^{-1}$ recorded by the BaBar experiment at the SLAC PEP-II
asymmetric-energy B Factory at a center-of-mass energy of $\sqrt{s} =
10.58$ GeV. We find no evidence
for a signal and set the 95% confidence level upper limits on the
cross sections to be $\sigma_{\mu\tau} <4.6$ fb
and $\sigma_{e\tau} <10.1$ fb. The ratio of the
cross sections with respect to the dimuon cross section are measured
to be $\sigma_{\mu\tau}/\sigma_{\mu\mu} < 4.0\times10^{-6}$ and
$\sigma_{e\tau}/\sigma_{\mu\mu} < 8.9\times10^{-6}$.
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