Determination of Leptoquark Properties in Polarized $e\gamma$ Collisions

We study leptoquark production using polarized $e\gamma$ colliders for the center of mass energies $\sqrt{s}=500$~GeV and 1~TeV. We show that using polarization asymmetries the ten different types of leptoquarks listed by Buchm"uller, R"uckl and Wyler can be distinquished from one another for leptoquark masses essentially up to the kinematic limit of the respective colliders. Thus, if a leptoquark were discovered an $e\gamma$ collider could play a crucial role in determining its origins.