  We perform a preliminary study of the deviations from the Standard Model
prediction for the cross section for the process $e \gamma \rightarrow \nu_e W
\gamma$. We work in the context of a higgsless chiral lagrangian model that
includes an extra vector resonance $V$ and an anomalous $\gamma W V$ coupling.
We find that this cross section can provide interesting constraints on the free
parameters of the model once it is measured in future $e \gamma$ colliders.
