This article is devoted to the study of the model - theoretic properties of special subclasses of Jonsson theories and their classes of models. Namely, introduce a new class of Jonsson theories is existentially prime convex Jonsson theories. The notion of convexity of theory was previously known, it was introduced by A.Robinson. The notion of existential simplicity introduced by the author of this article. Both conditions form a broad natural classes of theories. Thus two natural restrictions on Jonsson define a new class of theories with rich model - theoretic properties. Besides defined formulation of the problem, which define a new direction in the study Jonsson theories.