Abstract: Fuzzy automata plays an important part in automata theory and basic research. However, it is of pivotal importance to know how to construct the automata. A method for converting the generalized possibility LTL formulae into fuzzy alternating Büchi automata is worked out and then subjected to induction and proof test. The results show that the language recognized by fuzzy Büchi alternating automata is consistent with the language recognized by the generalized possibilistic LTL formulae.