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We investigate, in detail, a model in which the third family fermions aresubjected to an SU(2) dynamics different from the first two families.Constrained by the precision Z-pole data, the heavy gauge boson mass is boundedfrom below to be about 1.7 TeV at the $2\sigma$ level. The flavor-changingneutral current (FCNC) in the lepton sector can be significant in$\tau\leftrightarrow e$ and $\tau \leftrightarrow \mu$ transitions. In thelatter case, the ratio $Br(\tau\to \mu \bar{\nu_\mu} \nu_\tau)/ Br(\tau\to e\bar{\nu_e} \nu_\tau)$ and $Br(\tau\to \mu \mu \mu)$ can constrain the modelbetter than LEP/SLC data in some region of the parameter space. Furthermore,FCNCs are unavoidable in the quark sector. Significant effects to the$B^0-\bar{B^0}$ mixing and the rare decays of the K and B mesons, such as$K^\pm \to \pi^\pm \nu {\bar \nu}$, $b \to s \nu {\bar \nu}, B_s \to\tau^+\tau^-, \mu^+\mu^-$ and $B_{s,d} \to \mu^\pm \tau^\mp$, are expected.Comment: 42 pages, Latex, 2 ps figure

New physics in the third family and its effect on low-energy data