  Fermion compositeness and other new physics can be signalled by the presence
of a strong four-fermion contact interaction. Here we present a study of
$\ell\ell qq$ and $\ell\ell\ell'\ell'$ contact interactions using the
reactions: $\ell^+ \ell^- \to \ell'^+\ell'^-,b\bar b, c\bar c$ at future
$e^+e^-$ linear colliders with $\sqrt s=0.5-5$ TeV and $\mu^+\mu^-$ colliders
with $\sqrt s=0.5,4$ TeV. We find that very large compositeness scales can be
probed at these machines and that the use of polarized beams can unravel their
underlying helicity structure.
