Residual New Physics Effects in the Heavy Quark Sector, Tests at LEP2 and Higher Energies

We discuss the sensitivity of the processes $e^{+}{e}^{-}\to t\bar{t}$ and $e^{+}{e}^{-}\to b\bar{b}$ to special sets of operators describing residual New Physics effects. Experimental data in this sector together with those expected in the bosonic sector should allow to constrain possible New Physics schemes with effective scales in the 10 TeV range.