We study some of the consequences of the SU(6${)}_{\mathit{L}}$\ensuremath{\bigotimes}U(1${)}_{\mathit{Y}}$ model of unification of electroweak interactions and families with a horizontal gauge group SU(2${)}_{\mathit{H}}$, paying special attention to processes with flavor-changing neutral currents. We compute at the tree level the decays ${\mathit{K}}^{+}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{+}$${\mathrm{\ensuremath{\mu}}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, ${\mathit{K}}_{\mathit{L}}^{0}$\ensuremath{\rightarrow}${\mathrm{\ensuremath{\mu}}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\rightarrow}${\mathit{e}}^{\mathrm{\ensuremath{-}}}$\ensuremath{\nu}${\mathrm{\ifmmode\bar\else\textasciimacron\fi{}}}_{\mathit{e}}$${\ensuremath{\nu}}_{\mathrm{\ensuremath{\mu}}}$ from which we obtain lower bounds for the mass of the horizontal gauge boson associated with FCNC's. Finally we obtain limits on the mixing between ordinary and exotic charged leptons.