We propose possible methods to measure the nucleon electromagnetic formfactors in presence of two-photon exchange. Using a general parametrization ofthe spin structure of the matrix element for elastic $eN$-scattering, in termsof three independent complex amplitudes, we show that the measurements of thedifferential cross section for electron and positron nucleon elasticscattering, in the same kinematical conditions, allows to extract the nucleonelectromagnetic form factors. The same is correct for the polarization method,with the measurement of the $P_{x,z}$ components of the final nucleonpolarization (for the scattering of longitudinally polarized electrons andpositrons). An alternative way, in absence of positron beam, is to measure adefinite set of T-odd polarization observables, which includes three differentexperiments or only T-even observables, with five independent experiments. Inboth cases, the ratio $G_E(Q^2)/G_M(Q^2)$ is related to quantities of the orderof $\alpha$, which requires different polarization experiments of very highaccuracy.
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