The Boolean evolution functions consist in functions  : f0; 1gn-f0; 1gn that iterate (in discrete or continuous time) their coordinates i independently on each other, i 2 f1; :::; ng and they can be considered as representing Boolean dynamical systems with a variable structure. The concept of morphism is the usual one from the dynamical systems theory, adapted to the discrete, variable structure. A dual perspective is given by the Boolean antievolution functions, that di er from the evolution functions by the fact that time runs backwards. The concept of antimorphism reproduces the idea of morphism, corresponding to the situation when two systems run in opposite senses of time. Several de nitions of invariance of a set A  f0; 1gn are given, for Boolean evolution and antievolution functions. The purpose of the paper is that of showing in which manner the morphisms and the antimorphisms bring invariant sets in invariant sets.