Search for the Rare Leptonic Decays \boldmath \Blnu ($\ell e,\mu$)

We have performed a search for the rare leptonic decays \Bp \to \ellp \nul ($l=e,\mu$), using data collected at the \FourS resonance by the \babar\ detector at the \pep2 storage ring. In a sample of 468 million \BB pairs we find no evidence for a signal and set an upper limit on the branching fractions $\BR(\bmunu) < 1.0\times10^{-6}$ and $\BR(\benu) < 1.9\times10^{-6}$ at the 90% confidence level, using a Bayesian approach.