  In this paper we lay the basis of the theory of rational modules of corings
extending results on rational modules for coalgebras to the case of arbitrary
ground rings. We apply these results mainly to categories of entwined modules
(e.g. Doi-Koppinen modules, alternative Doi-Koppinen modules) generalizing
results of Y. Doi, M. Koppinen and C. Menini et al. on the categries of
Doi-Hopf moduels and categories of relative Hopf modules.
