The functional differential equation with state-dependent delay x′(t)=f(t

x(t-r(xt)))

was considered and the basic properties of its solution that satisfying the initial conditions x0=φ

in which f:[0

∞)×R→R

φ∈C

was studied by using the method of steps.By constructing the iterative sequence

the existence of unique solution of this equation with initial value conditions in the interval [-h

∞) was obtained

and it was Lipschitz continuous.The above work extends the corresponding results from H.O.Walther.