The tasks of concept formation for Russian society modernization have be-come more acute under conditions of global competition thus asking for a more active reac-tion of academic community. In the paper, some not trivial by far aspects of the issue arepresented. Nonlinear character of modernization process is shown, and a mini-max strategyfor Russia is suggested: priority for human bads minimization, first of all, for unbearabletribulations suffered by a considerable fraction of population, while, at the same time, as faras possible, increasing social goods of greatest significance for vital functions of over 50%majorities of population. To implement this strategy, institutional regulative rules have tobe changed for vital activities of all population strata including higher levels of the politicaland business elites allowing for an integrated and coordinated implementation of interrelatedtechnical, technological, social and economic as well as social cultural changes. This how-ever ought to be done notper saltumbut incrementally and differentially both nationwide andin each region considering real state of its modernization. Three basic stages of integrat-ed modernization of Russian society are offered, as well as preliminary identification of the Russian Federation subjects with these stages.