In this work fundamental interactions of type wave-particles are discussed. Main object of the investigation is surfatron accelerations of the protons by sin- gle electromagnetic wave. The surfatron effect of protons acceleration is inves- tigated through numerical simulations, on the basis of nonlinear, nonstationary, second order differential equation for the wave phase at the charged particle’s trajectory. The temporal dynamics of protons surfatron acceleration for differ- ent variants of the initial parameters are studied. The optimal conditions for maximum ultrarelativistic particles surfatron acceleration by the electromag- netic wave in space plasma are considered. An analytical approximation for protons energy strong growth was done. © 2016, Academic Publishing House. All rights reserved.