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The purpose of this paper is to offer the theory of a parametrical regulation of market economy development, and the results of the theory development and usage.

Theoretical results of the abstract have been obtained by way of applying the theory of ordinary differential equations, geometrical methods in variation tasks and the theory of dynamic systems. These results have been used for solving a number of practical tasks.

The market economy development parametrical regulation theory structure has been offered. The approach to parametrical regulation of a nonlinear dynamic system's development has been suggested. An assumption about the existence of solution to the task of calculus of variations on the choice of the optimum laws of parametrical regulation within the given finite set of algorithms has been set forward. An assumption about the conditions sufficient for the existence of an extremal's bifurcation point of the task of calculus of variations on the choice of the optimum laws of parametrical regulation within the given finite set of algorithms is presented, formulated and proved. Theory application samples have been provided.

Future papers would be focused on studies of rigidness of other mathematic models of economic systems.

The research findings could be applied to the choice and realization of an effective budget and tax as well as monetary and loan state policy.

The market economy development parametrical regulation theory has been offered for consideration for the first time.