We consider the fold complementarity problem, which is one of the recent subjects in complementarity theory. It is a mathematical model used in economics in the study of distributive problems [\textit{A. Villar}, Operator theorems with applications to distributive problems and equilibrium models, Lecture Notes in Economics and Mathematical Systems 377, Springer-Verlag Berlin (1992; Zbl 0781.90016)]. A particular case is the \(k\)-fold complementarity problem, studied using a variant of the notion of \(Z\)-function by \textit{A. Villar} [loc. cit.]. In this way, Villar obtained the solution of this problem as a solution of a minimization problem. We study the fold complementarity problem by a topological method. We show that this method is also applicable to systems of fold complementarity problems.