Zγ H Vertex Effects at Future Colliders

We show that the Higgs production in $e\gamma$ collisions, through the one-loop reaction $e\gamma\to eH$ at large transverse momentum, can provide a precise determination of the $Z\gamma H$ vertex. We concentrate on the analysis of signal rates vs background looking for strategies to improve the ratio $S/B$. Possible bounds on anomalous contributions to the $Z\gamma H$ vertex are derived.