In the first part of the paper, we prove a generalization of the classical Poincare-Miranda theorem to the case of a denumerable set of continuous functions of denumerable number of variables. The second part of the paper concerns the controllability of nonlinear repetitive processes. First, we formulate a theorem on the existence of a unique solution to such process and theorem on the continuous dependence of solutions on controls. Next, we use the obtained generalization of Poincare-Miranda theorem to prove a result on the controllability of nonlinear repetitive process.