We are studying the electron scattering process e p to e p gamma in order to obtain information on the genuine virtual Compton scattering (VCS) process gamma^* N to gamma N. In addition to the two kinematical variables of real Compton scattering, e.g. the scattering angle theta and the energy omega of the outgoing photon, the invariant amplitude for VCS depends on a third kinematical variable, which we choose as the absolute value of the three-momentum transfer to the nucleon. The structure-dependent coefficients in the VCS amplitude therefore acquire a momentum dependence and are termed ``generalized polarizabilities of the nucleon in analogy to real Compton scattering. Utilizing the heavy baryon formalism of chiral perturbation theory we present predictions for the momentum dependence of the ``generalized polarizabilities and discuss the VCS response functions to be measured in the scheduled electron scattering experiments.
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