Production of neutral and charged Higgs bosons of the MSSM at the future e-gamma colliders

A complete study for the production of neutral (h^0, H^0, A^0 (= \phi^0_i)) and charged Higgs (H^\pm) bosons at electron-photon colliders is presented in the context of the minimal supersymmetric standard model. A particular choice of the non-linear R_\xi gauge is used to evaluate the amplitudes of the reaction e-gamma --> e \phi^0_i. The resulting cross section indicates that it will be possible to detect a signal from the neutral Higgs bosons for most regions of parameter space at the future linear colliders with \sqrt{s}=500 GeV through the reaction e gamma --> e \phi^0_i. This reaction also offers the interesting possibility to measure the Higgs mass through the detection of the outgoing electron. The production of the charged Higgs boson through the reaction e gamma --> \nu_e H^\pm$ has in general smaller values for the cross section, which seems more difficult to observe.