  We consider the possibility of studying anomalous contributions to the
gamma-gamma-H and Z-gamma-H vertices through the process e-gamma--> e-H at
future e-gamma linear colliders, with Sqrt(S)=500-1500 GeV. We make a model
independent analysis based on SU(2)xU(1) invariant effective operators of dim=6
added to the standard model lagrangian. We consider a light Higgs boson (mostly
decaying in bar(b)-b pairs), and include all the relevant backgrounds. Initial
e-beam polarization effects are also analyzed. We find that the process
e-gamma--> e-H provides an excellent opportunity to strongly constrain both the
CP-even and the CP-odd anomalous contributions to the gamma-gamma-H and
Z-gamma-H vertices.
