Among non-monotonic systems of reasoning, non-monotonic modal logics, and autoepistemic logic in particular, have had considerable success. The presence of explicit modal operators allows flexibility in the embedding of other approaches. Also several theoretical results of interest have been established concerning these logics. In this paper we introduce non-monotonic modal logics based on many-valued logics, rather than on classical logic. This extends earlier work of ours on many-valued modal logics. Intended applications are to situations involving several reasoners, not just one as in the standard development. 1 Introduction Several kinds of non-monotonic logics have been considered over the past dozen years. Among these, non-monotonic modal logics have been particularly interesting. These, of course, have explicitly occurring modal operators, and this allows for fine control when translating from other formalisms; see [13, 5], for instance. Following the ideas of McDermott and Do..