Asymptotic Behavior of Nucleon Electromagnetic Form Factors in Space- and Time-Like Regions

We compare the existing data about electromagnetic form factors of the proton in the time-like region of momentum transfer (up to $q^2\simeq$ 14 (GeV/c)$^2$), with the corresponding data in the space-like region. From the constrains given by the Phragm\`en-Lindel\"of theorem, it turns out that the asymptotic regime can not be reached simultaneously for both form factors (electric and magnetic) in the considered region of momentum transfer. The angular dependence for the annihilation processes, such as $\bar{p}+p\leftrightarrow e^++e^-$, is sensitive to the asymptotic properties of form factors and to the two-photon physics in the time-like region.