  We list all possible dimension-six CP-conserving $SU_c(3)\times SU_L(2)
\times U_Y(1)$ invariant operators involving the third-family quarks which
could be generated by new physics at a higher scale. Expressions for these
operators after electroweak gauge symmetry breaking and the induced effective
couplings $Wt\bar b$, $Xb\bar b$ and $Xt\bar t$ $( X=Z,\gamma,g,H)$ are
presented. Analytic expressions for the tree level contributions of all these
operators to the observables $R_b$ and $A^b_{FB}$ at LEP I,
$\sigma(e^+e^-\rightarrow b\bar b)$ and $A^b_{FB}$ at LEP II,
$\sigma(e^+e^-\rightarrow t\bar t)$ and $A_{FB}^t$ at the NLC, as well as
$\sigma(p\bar p\rightarrow t\bar b+X)$ at the Tevatron upgrade, are provided.
The effects of these operators on different electroweak observables are
discussed and numerical examples presented. Numerical analyses show that in the
coupling region allowed by $R_b$ and $A^b_{FB}$ at LEP I, some of the new
physics operators can still have significant contributions at LEP II, the
Tevatron and the NLC.
