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