Well-posedness of the Cauchy problem for one class functional differential equation

For the nonlinear functional differential equations with distributed and concerted delays theorems on the continuous dependence of the solution on perturbations of the initial data and the right-hand side of equation are proved (well-posedness of the Cauchy problem). Under initial data we understand the collection of initial moment, of delay parameters and initial function. Perturbations of the right-hand side of equation are small in the integral sense and perturbations of the initial data are small a standard norm.