There is a general agreement that speaking requires attention at least for conceptual and lexical processes of utterance production. However, conflicting results have been obtained with dual-task paradigms using either repetition tasks or more generally tasks involving limited loading of lexical selection. This study aimed to investigate whether post-lexical processes recruit attentional resources. We used a new dual-task paradigm in a set of experiments where a continuous verbal production task involved either high or low demand on lexical selection processes. Experiment 1 evaluates lexical and post-lexical processes with a semantic verbal fluency task, whereas Experiments 2 and 3 focus on post-lexical processes with a non-propositional speech task. In each experiment, two types of non-verbal secondary tasks were used: processing speed (simple manual reaction times) or inhibition (Go/No-go). In Experiment 1, a dual-task cost was observed on the semantic verbal fluency task and each non-verbal task. In Experiment 2, a dual-task cost appeared on the non-verbal tasks but not on the speech task. The same paradigm was used with older adults (Experiment 3), as increased effort in post-lexical processes has been associated with ageing. For older adults, a dual-task cost was also observed on the non-propositional verbal task when speech was produced with the inhibition non-verbal task. The results suggest an attentional cost on post-lexical processes and strategic effects in the resolution of the dual-task.