In the present work our attention is turned to those Jonnson classes of models which are classes of models of theories which have model completions. Main reason for that lies in the fact that the class of models of a theory which has the model completion is almost a Jonnson class, therefore that part of model theory which concern model completions may be applied in full power. In such sense this paper is closly related to the works of others as of M. Yasuhara , Comfort-Negreponties  etc. (relatively complete list of references on the subject can be found in the works just cited). The terminology that is used in this paper is mostly according to  and , however we repeat some of it, since it is not uniquely determined in general, and also some assumptions and conventions are introduced.