Purpose: Digital natives constitute a substantial part of consumers nowadays. Yet, a theoretical understanding of the factors driving their engagement with new-age digital services is lacking. This study therefore aims to examine digital natives’ continuance usage of the proliferating over-the-top (OTT) services. To address these objectives, the study uses a comprehensive model that primarily integrates perceived value, cognitive absorption and customer brand engagement theories. Design/methodology/approach: Data were collected using an online personal questionnaire targeting active digital natives OTT service users using the online software tool SurveyMonkey. A sample of 1,415 digital natives was analysed using structural equation modelling. Findings: The findings indicated that continuance usage is predicted by all three theories. The results illustrate that cognitive absorption and customer brand engagement are the most critical in enhancing continuance usage. Gender effects on digital natives’ value perceptions were found. The model explains 57% of the variance in users’ continuance usage. Originality/value: The study adds valuable contributions to the existing literature that are relevant to digital natives’ engagement with new-age digital services. The proposed integrated model and the role of gender in value formations provide managers with novel insights when designing effective strategies to increase continuance usage for the largest consuming generation. Peer review: The peer review history for this article is available at: https://publons.com/publon/10.1108/OIR-03-2022-0133.