Excited Leptonic States in Polarized e^-\gamma and e^+ e^- Collisions

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.