On the Chaplygin method for the Darboux problem

In the paper we deal with the Darboux problem for hyperbolic functional differential equations. We give the sufficient conditions for the existence of the sequence $\{z^{(m)}\}$ such that if $\tilde{z}$ is a classical solution of the original problem then $\{z^{(m)}\}$ is uniformly convergent to z$\tilde{z}$. The convergence that we get is of the Newton type.