Query languages for retrieving information from disjunctive databases are an interesting open area of research. In this paper we study the expressive power of major nonmonotonic formalisms — such as circumscription, default logic, autoepistemic logic and some logic programming languages — used as query languages over disjunctive databases. For this aim, we define the semantics of query expressions formulated in different nonmonotonic logics. The expressive power of the languages that we consider has been explored in the context of relational databases. Here, we extend this study to disjunctive databases; as a result, we obtain a finer-grained characterization of the expressiveness of those languages and interesting fragments thereof. For instance, we show that there exist simple queries that cannot be expressed by any preferential semantics (including the minimal model semantics and the various forms of circumscription), while they can be expressed in default and autoepistemic logic. Secondly, we show that default logic, autoepistemic logic and some of their fragments express the same class of Boolean queries, which turns out to be a strict subclass of the ∑^p₂-recognizable Boolean queries. The latter result is proved by means of a new technique, based on a counting argument. Then we prove that under the assumption that the database consists of clauses whose length is bounded by some constant, default logic and autoepistemic logic express all of the ∑^p₂-recognizable Boolean queries, while preference-based logics cannot. These results hold for brave reasoning; we obtain dual results for cautious reasoning. Our results appear to be interesting both in the area of database theory and in the area of knowledge representation.