The standard Marcus theory of charge transfer reaction in solution, relying on a Gaussian solvation picture, or, equivalently, on a linear response approximation, and involving two parameters, the reorganization energy and the reaction free-energy parameter, may fail when the solvation has a different character in the reactant and product state. We propose two complementary. theoretical extensions of Marcus theory applying to those cases, based either on a two-Gaussian-states solvation picture, or on a non-Gaussian solvation picture. As illustration, we show that such situations arise even for simple half oxido-reduction reactions involving the Cu+/Cu2+ or Ag-0/Ag+ couples, for which electron transfer free-energy surfaces have been generated using first-principle molecular dynamics simulations. The two theoretical extensions are shown to exhibit the correct nonlinear response behavior and to reproduce the simulation results quantitatively, whereas a simple one-Gaussian-state Marcus description breaks down.