English has several periphrastic verbal forms that are semantically close to particular modal verbs and perform suppletive functions in relation to them. After an exploration of the properties of potential periphrastic forms, this study investigates the nature of the relationship between the modals must, should, will and can and various semantically close periphrastics. The focus is on the pragmatic interpretation of the items compared, with some attention to their functions in discourse. Despite the relative idiosyncracy of all these items, the general marked status of periphrastics is evident, and this is shown to be reflected in a number of different ways. Level of formality is a further differentiating factor here.