In this work we study the optimal control problem for a class of nonlinear time-delay
systems via paratingent equation with delayed argument. We use an equivalence theorem
between solutions of differential inclusions with time-delay and solutions of paratingent
equations with delayed argument. We study the problem of optimal control which minimizes a
certain cost function. To show the existence of optimal control, we use the main
topological properties of the set solutions of paratingent equation with delayed
argument