<p>In this paper, we consider an optimal control problem involving delays in phase variables and controlled discontinuities of phase trajectories. To solve problems of this type, we propose the parametrization method based on representing control functions as generalized splines with movable nodes and subsequently reducing the original problem to a finite-dimensional nonlinear programming problem for control parameters. In this work, the moments of discontinuity of the phase trajectory are considered as variables of the resulting finite-dimensional problem. Also, we propose an algorithm for calculating the derivatives of the objective function based on the use of the adjoint variables of the original optimal control problem. The algorithm proposed for solving the considered problems was tested by examples presented in the work.</p>