Abstract In this paper, we will investigate further fuzzy measures and fuzzy integrals given by Sugeno (1974). Our purpose is concentrated on the convergence of sequences of fuzzy measures or fuzzy integrals. Some concepts such as “convergence”, “uniform convergence”, “convergence in integral”, “weak convergence” are introduced for the sequence of fuzzy measures. Then the properties and relations of them are discussed. Furthermore, various kinds of convergence theorems of fuzzy integrals are extended. These are generalized monotone convergence theorem, generalized Fatou's lemma, etc.