The aim of this paper is to analyze the syntactic and semantic process of grammaticalization of quasi-homonym periphrastic constructions "deber + infinitive", "deber a + infinitive" and "deber de + infinitive", which behave in a peculiar way. While the first came to denote the deontic modality, the second developed the epistemic variant, and the last one acquired meanings of immediate future. Also, basing the study on the medieval and classical literary texts, the author pretends to demonstrate the causes of the disappearance of forms still prevalent and abundant in the sixteenth century.