On solvability of essentially degenerate nonlinear algebraic differential system

We consider nonlinear system of ordinary differential equations, which is not solved with respect to the derivative of the desired vector function and identically degenerate in the domain of definition. Under the assumption that the initial data generate a solution of the maltiplicity grater than one for the corresponding finite-dimensional system, the process of transformation of the given system into the system in the normal form is suggested, the theorem of existence of a solution to a Cauchy problem is proved.