New BaBar Results on Rare Leptonic B Decays

New preliminary BaBar results for rare leptonic decays $B^- \to K^-\nu \bar{\nu}$ and $B^0\to \ell^+\ell^-$ are reported. Using data collected at the $\FourS$ with the BaBar detector, no evidence for a signal was found yielding the corresponding upper limits at the 90% confidence level: ${\cal B}(B^-\to K^-\nu \bar{\nu})< 9.4 \times 10^{-5}$ for $50.7 \invfb$, ${\cal B}(\bee)< \eeul$, ${\cal B}(\bmm) < \mmul$ and ${\cal B}(\bem) < \emul$ using $54.4 \invfb$.