This paper contains the formulation of the method announced in [1] for describing the complete evolution of a large dynamical system inside a single subdynamics. This subdynamics may be of use in field theoretical models, in optical systems, and in the statistical mechanical treatment of gases and solids.  There is no loss of information when the number of degrees of freedom is extended to infinity.  The original dynamics is first widened by distinguishing, on a physical basis, between categories of degrees of freedom. Once an appropriate concept of vacuum state is introduced by reference to the observation conditions, the redundant self-energy degrees of freedom are eliminated by keeping only the vacuum subdynamics. The evolution is given through quasi-kinetic equations, which exhibit an historical character - a first step toward irreversibility - but respect the completeness of the description.