This study investigates the role of locality (a task/material‐related variable), demographic factors (age, education, and sex), cognitive capacities (verbal working memory [WM], verbal short‐term memory [STM], speed of processing [SOP], and inhibition), and morphosyntactic category (time reference and grammatical aspect) in verb‐related morphosyntactic production (VRMP). A sentence completion task tapping production of time reference and grammatical aspect in local and nonlocal configurations, and cognitive tasks measuring verbal WM capacity, verbal STM capacity, motor SOP, perceptual SOP, and inhibition were administered to 200 neurotypical Greek‐speaking participants, aged between 19 and 80 years. We fitted generalized linear mixed‐effects models and performed path analyses. Significant main effects of locality, age, education, verbal WM capacity, motor SOP, and morphosyntactic category emerged. Production of time reference and aspect did not interact with any of the significant factors (i.e., age, education, verbal WM capacity, motor SOP, and locality), and locality did not interact with any memory system. Path analyses revealed that the relationships between age and VRMP, and between education and VRMP were partly mediated by verbal WM; and the relationship between verbal WM and VRMP was partly mediated by perceptual SOP. Results suggest that subject‐, task/material‐ and morphosyntactic category‐specific factors determine accuracy performance on VRMP; and the effects of age, education, and verbal WM on VRMP are partly indirect. The fact that there was a significant main effect of verbal WM but not of verbal STM on accuracy performance in the VRMP task suggests that it is predominantly the processing component (and not the storage component) of verbal WM that supports VRMP. Lastly, we interpret the results as suggesting that VRMP is also supported by a procedural memory system whose efficiency might be reflected in years of formal education.