  We compute the MSSM one-loop contributions to the asymptotic energy behaviour
of fermion-antifermion pair production at future lepton-antilepton colliders.
Besides the conventional logarithms of Renormalization Group origin, extra SUSY
linear logarithmic terms appear of "Sudakov-type". In the TeV range their
overall effect on a variety of observables can be quite relevant and
drastically different from that obtained in the SM case.
