We examine the sensitivity of the process e gamma --> nuq + X to W' bosons
which arise in various extensions of the standard model. We consider photon
spectra from both the Weizsacker-Williams process and from a backscattered
laser. The process is found to be sensitive to W' masses up to several TeV
, depending on the model, the center of mass energy, the integrated luminos
ity, and assumptions regarding systematic errors. If extra gauge bosons wer
e discovered first in other experiments, the process could also be used to
measure W' couplings. This measurement would provide information that could
be used to unravel the underlying theory, complementary to measurements at
the CERN Large Hadron Collider.