Complexity theory and nonequilibrium space plasmas dynamics. The case of Solar Wind CME effects. Georgios P.Pavlos1 1 Democritus University of Thrace, Xanthi, Greece Near equilibrium space plasmas can be described by the Boltzmann – Gibbs’ statistical theory and the corresponding entropy principle related to the normal diffusion theory. Also, the physics of the near equilibrium states of space plasmas includes Gaussian statistical behavior as well as smooth macroscopic dynamics corresponding to the smooth MHD theory or the known Langevin and Fokker-Planck equations of the mesoscopic level. However, as the plasma system deviates from the near equilibrium state we can observe the emergence of new physics which is created by the extension of the statistical theory and the entropy principle. So far Tsallis nonextensive statistical theory and Tsallis extension of the Boltzman-Gibbs entropy principle to the q-entropy principle reveals strong universality character concerning non equilibrium dynamics. Tsallis q-entropy principle can explain the emergence of a series of new and significant physical characteristics in distributed systems as well as in space plasmas. Such characteristics are: non Gaussian statistics and anomalous diffusion processes, strange and fractional dynamics, multifractal, percolating and intermittent turbulence structures, multiscale and long spatio temporal correlations, fractional acceleration and Non Equilibrium Stationary States(NESS) or non equilibrium self organization process and non equilibrium phase transition an topological phase transition processes. In this study, we present some new and significant results concerning the dynamics of Coronal mass ejections (CMEs) observed in the near Earth solar wind system. Especially we estimated the Tsallis qtriplet statistical parameters of Tsallis non extensive statistics, as well as other dynamical characteristics of the solar wind system during quiet and CMEs periods. Our results are in faithful agreement with the predictions of complexity theory and the non extensive statistical theory of Tsallis.