Adequacy of the description of flow and transport processes in subsurface depends on how well a model represents the heterogeneity. One of the simplest models to describe the heterogeneity structure is a so-called composite system. Flow and transport simulation in composite systems can be reduced to solving equations and averaging the solutions. A different approach related to averaging the equations leads to new equations. This description is designated as monocontinuum description. If the homogeneous components of a composite system, so-called phases, have different hydrodynamic and/or geometric parameters, it is natural to study averaging on the individual phases along with the global averaging. This approach takes into consideration the mean fields in the individual continuum phase as well as the cross flows and cross forces between continua. However, this description is nonclosed. To overcome this difficulty, the phenomenological theory usually postulates a special interaction mechanism for closing the equations. This paper presents the exact equations of mass balance and moment balance for each phase. The exact sense of exchange terms in the multicontinuum models is explained. We demonstrate that joint consideration of the monocontinual and multicontinual systems in the case of two-phase random composite leads to a closed description and that we can find the exchange terms. For a periodic composite system the same approach leads to a closed description for any number of phases. The terms describing the interactions between continua for systems with a random and periodical structure are calculated. We examine the hypothesis customarily made in the phenomenological models. ¿ 2000 American Geophysical Union