In order to establish a typological picture of periphrastic negation, this chapter begins from the criteria for periphrasis established by Ackerman and Stump. These are feature intersection, non-compositionality, and distributed exponence. It is argued that while the first two work well for defining periphrasis, the third criterion is not sufficiently robust, and should therefore be substituted by the criterion of multiple exponence. Multiple exponence is a recurrent feature of morphology and therefore, when found in a syntactic construction, it signals its morphology-like status. The chapter analyses the applicability of the criteria by testing them on data from genetically and typologically diverse languages (such as Japanese, and languages within Oto-Manguean, Nilotic, Tungusic, Uralic, Nakh-Daghestanian, and Semitic languages). It shows the extent to which the existing criteria can be applied to languages of different types, and justifies the new criterion (multiple exponence) for identifying periphrasis.