  We analyze the capability of the next generation of linear electron--positron
colliders to unravel the spin and couplings of excited leptons predicted by
composite models. Assuming that these machines will be able to operate both in
the $e^+e^-$ and $e^-\gamma$ modes, we study the effects of the excited
electrons of spin $\frac{1}{2}$ and $\frac{3}{2}$ in the reactions $e^-\gamma
\rightarrow e^-\gamma$ and $e^+e^- \rightarrow \gamma\gamma$. We show how the
use of polarized beams is able not only to increase the reach of these
machines, but also to determine the spin and couplings of the excited states.
