In this paper we introduce the notion of Fuzzy ω-Automata as an accepting device for Fuzzy ω-languages. We define Fuzzy ω-Finite State Automata which accept Fuzzy ω-regular languages with different acceptance criteria. We also define Distributed Fuzzy ω-Finite State Automata which are a group of fuzzy ω-finite state automata working in unison to accept a language with different modes of acceptance like the t-mode, *-mode, = k-mode, ≤k-mode and ≥k-mode. We prove that Distributed Fuzzy ω-Finite State Automata accept the same set of languages as Fuzzy ω-Finite State Automata. Analogously we define Fuzzy ω-Pushdown Automata and Distributed Fuzzy ω-Pushdown Automata along with the different acceptance criteria and modes of acceptance for the distributed case. The class of languages accepted by Fuzzy ω-Pushdown Automata is fuzzy CFLω while the class of languages accepted by Distributed Fuzzy ω-Pushdown Automata contains CFLω. We give proofs to show that all modes of acceptance are equal in the case of Distributed Fuzzy ω-Pushdown Automata. We also define L-Fuzzy ω-Automata and give some examples to show how it can be used to accept some non-fuzzy languages which are not accepted by their classical counterparts. © 2001 Elsevier Science Inc. All rights reserved.