Data taken by the Mark II detector at the SLAC e+e- storage ring PEP was used to search for exclusive decays of D and B mesons into two charged leptons plus a charged pion or kaon. All possible charge and lepton combinations consistent with charge conservation were considered and no evidence for any signals was found. We obtain upper limits for the various branching ratios ranging from 2.5×10-3 to 9.2×10-3, at a 90% confidence level. Some of these limits can be used to constrain leptoquark masses in various models. © 1990 The American Physical Society.