We prove a theorem of existence and uniqueness of the solution of a Cauchy problem (j) for nonlinear partial differential equation of the first order with a hereditary structure. We associate to (j) problem a sequence of Cauchy problems without functional argument. The solutions z_n of these problems are established by Baiada's approximation method. Finally the solution of problem (j) is given as a limit surface of the sequence (z_n)_n. The present result extends the existence theorem given by Z. Kamont in the linear case [Ann. Polon. Math. 35 (1977/78), no. 1, 27–48].
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