  We study the flavor physics in two extensions of the quark sector of the
Standard Model (SM): a four generation model and a model with a single
vector--like down--type quark (VDQ). In our analysis we take into account the
experimental constraints from tree--level charged current processes, rare Kaon
decay processes, rare B decay processes, the $Z\to b \bar{b}$ decay, $K$, $B$
and $D$ mass differences, and the CP violating parameters $\frac
\epsilon^\prime}{\epsilon}$, $\epsilon_K$ and $a_{\psi K}$. All the constraints
are taken at two sigma. We find bounds on parameters which can be used to
represent the New Physics contributions in these models ($\lambda_{t^
\prime}^{bd}$, $\lambda_{t^ \prime}^{bs}$ and $\lambda_{t^ \prime}^{sd}$ in the
four--generation model, and $U_{bd}$, $U_{bs}$ and $U_{sd}$ in the VDQ model)
due to all the above constraints. In both models the predicted ranges for
$a_{SL}$ (the CP asymmetry in semi-leptonic decays), $\Delta M_D$,
$B(K^+\to\pi^+ \nu \bar{\nu})$, $B(K_L\to\pi^0 \nu \bar{\nu})$ and $B(K_L\to
\mu \bar{\mu})_{SD}$ can be significantly higher than the predictions of the
SM, while the allowed ranges for $a_{\psi K}$ and for $\Delta m_{B_S}$ are
consistent with the SM prediction.
