Summary: When a uniform substitution is applied to a word, the same letter at different positions in the word is transformed everywhere in the same way. Thus, a uniform substitution \(S_ H\) is determined by a set \(H\) of homomorphisms. We define recognizable and rational sets of homomorphisms and we prove closure and non-closure properties of the class of languages of the form \(S_ H(L)\), where \(L\) is regular and \(H\) is recognizable. We also show that in this case (and in more general situations as well) the membership problem for \(S_ H(L)\) is solvable in deterministic polynomial time.