The paper deals with a boundary value problem for quasilinear differential-functional systems in the Schauder canonic form. The author proves, by means of the fixed point theorem in the product of two Banach spaces, existence, uniqueness and continuous dependence on boundary data of generalized solutions (in the “almost everywhere” sense). A few kinds of differential-integral systems and systems with a retarded argument can be obtained from the considered problem by specializing the operators in the differential-functional systems.