  An interesting extension of the Standard Model is based on the electroweak
gauge group SU(3)_L x U(1). It requires three generations to cancel anomalies,
treats the third generation differently than the first two, and has a rich
phenomenology. There are several models, distinguished by the embedding of the
charge operator into the SU(3)_L group and by the choice of fermion
representations. In this Brief Report, we consider flavor-changing neutral
currents in these models, concentrating on the P-Pbar mass difference, where
P=(K, D, B, B_s), as well as B --> K l^+ l^-, B --> mu^+ mu^- and B_s --> mu^+
mu^- decays. Although the P-Pbar mass difference has been considered previously
in some models, the rare B decays are new. We find that the strongest bounds
come from the B-Bbar and Bs-Bs-bar mass differences.
