What brings young children to gradually replace single-word with multiword utterances? The Cognitive-Pragmatic Model (CPM) is elaborated to answer this question. It is based on the idea that single-word utterances are a well-established behaviour and considers that the change from single-word to multiword speech requires a conceptual change in the way children apprehend the relationship between communicative intentions and their verbal expression. The CPM proposes that two phenomena, expressive options and co-constructed Sucessive Single-Word Utterances (SSWUs) - Conversationally-generated and discourse-sustained Child-generated -, provide the initial steps in the transition towards multiword speech. The CPM predicts that children (1) start showing expressive options and producing Conversationally-generated and Child-generated SSWUs sustained by immediately previous discourse; (2) all kinds of SSWUs appear before multiword utterances; (3) across-turns Child-generated SSWUs appear before within-turn Child-generated SSWUs; and (4) before multiword utterances become dominant, children rely often on conversation and/or on immediately previous discourse to produce SSWUs or multiword utterances. The predictions of the Cognitive Pragmatic Model are confirmed by the longitudinal data of two French-acquiring children observed during spontaneously occurring interaction. The implications of the Cognitive Pragmatic Model and issues requiring further investigation are identified and discussed.