  We present a search for the decays B0->e+e-, B0->mu+mu-, and B0->e+- mu-+ in
data collected at the Y(4S) resonance with the Babar detector at the SLAC B
Factory. Using a data set of 111 fb^-1, we find no evidence for a signal in any
of the three channels investigated and set the following branching fraction
upper limits at the 90% confidence level: B(B0->e+e-)< 6.1 x 10^-8,
B(B0->mu+mu-) < 8.3 x 10^-8, and B(B0->e+-mu-+) < 18 x 10^-8.
