DARK ENERGY DYNAMICAL DOMINATION IN LOCAL FLOWS OF GALAXIES A.D. Chernin Sternberg Astronomical Institute, Moscow University, Moscow, Russia We demonstrate that the general theory of relativity with non-zero dark energy controls the dynamics of the Local Group of galaxies and the expansion flow of galaxies around the group at the distances of 1-3 Mpc from us. The weak field approximation is valid on these spatial scales. In terms of classical mechanics, it enables to predict (Chernin 2001, Byrd et al. 2012) that Newton's attraction force produced by matter (dark matter and baryons) dominates in the group, while Einstein's repulsion force produced by dark energy background (in which both group and flow are embedded) dominates in the flow. It is due to the dark energy domination that the flow has a nearly linear velocity-distance relation. HST observations (Karachentsev et al. 2003, 2013) show that a dozen of groups with flows in the nearby volume of about 20 Mpc across reveal the same regular dynamical structure. Local dark energy domination is a new phenomenon of nature. In combination with the global cosmological expansion, it reveals the universal character of general relativity dynamics. ==========================================================================