A system of two generalized variational inequalities, based on the variational inequalities introduced by

*G. Stampacchia* [C. R. Acad. Sci., Paris 258, 4413–4416 (1964;

Zbl 0124.06401)] in the early sixties, is considered. An iterative algorithm to approximate the solution of the system is developed using the idea of a fixed point for a corresponding nonexpansive operator. Strong convergence theorems are established in the framework of real Banach spaces.