  We discuss electron-electron contact-interaction searches in the Bhabha and
Moller processes at planned Linear Colliders run in the electron-positron and
electron-electron modes, with longitudinally polarized beams. Our analysis is
based on the measurement, for the two processes, of polarized differential
cross sections that allow to disentangle the different, independent,
four-fermion couplings. We evaluate by a model-independent analysis the
sensitivities to the contact coupling constants, emphasizing the role of the
available beam polarization and the complementarity of the two processes in
giving the best limits. We also make a comparison with the potential of
$e^+e^-\to\mu^+\mu^-$ at the same energy and beams polarization.
