Summary: Variation formulas of solution are obtained for linear with respect to prehistory of the phase velocity neutral functional-differential equations with variable delays and with discontinuous initial condition. In the variation formulas are detected the effects of perturbation of delay function entering in the phase coordinates and the discontinuous initial condition. Variation formula of solution plays the basic role in proving necessary conditions of optimality and under sensitivity analysis of mathematical models. Discontinuity of the initial condition means that the values of the initial function and the trajectory, in general, do not coincide at the initial moment.