We present a search for the decays B0 --> e+e-, B0 --> mu+ mu- and B0 --> e mu using data collected with the BABAR detector at the PEP-II e+e-collider at SLAC. Using a dataset corresponding to 384 x 10^6 BBbar pairs, we do not find evidence of any of the three decay modes. We obtain upper limit on the branching fractions, at 90% confidence level, of B(B0 --> e+e-) mu+ mu-) e mu) < 9.2 x 10^{-8}.

Comment: 8 pages, 14 postscript figures