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
ββqq and ββββ²ββ² contact interactions using the
reactions: β+βββββ²+ββ²β,bbΛ,ccΛ at future
e+eβ linear colliders with sβ=0.5β5 TeV and ΞΌ+ΞΌβ colliders
with sβ=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.Comment: 12 pg, to appear in the {\it Proceedings of the 1996 DPF/DPB Summer
Study on New Directions for High Energy Physics - Snowmass96}, Snowmass, CO,
25 June - 12 July, 199