  We consider single production of leptoquarks (LQ's) at $e\gamma$ colliders,
for two values of the centre-of-mass energy, $\sqrt{s}=500$ GeV and 1 TeV. LQ's
with masses essentially up to the kinematic limit can be seen, even for
couplings as weak as $O(10^{-3})$-$O(10^{-2})\alpha_{em}$. It is possible to
detect LQ's of mass greater than $\sqrt{s}$ by looking for signals of virtual
LQ production in $e\gamma\to e q{\overline q}$.
