Activity recognition is essential in providing activity assistance for users in smart homes. While significant progress has been made for single-user single-activity recognition, it still remains a challenge to carry out real-time progressive composite activity recognition. This paper introduces a hybrid ontological and temporal approach to composite activity modelling and recognition by extending existing ontology-based knowledge-driven approach. The compelling feature of the approach is that it combines ontological and temporal knowledge representation formalisms to provide powerful representation capabilities for activity modelling. The paper describes in detail ontological activity modelling which establishes relationships between activities and their involved entities, and temporal activity modelling which defines relationships between constituent activities of a composite activity. As an essential part of the model, the paper also presents methods for developing temporal entailment rules to support the interpretation and inference of composite activities. In addition, this paper outlines an integrated architecture for composite activity recognition and elaborated a unified activity recognition algorithm which can support the recognition of simple and composite activities. The approach has been implemented in a feature-rich prototype system upon which testing and evaluation have been conducted. Initial experimental results have shown average recognition accuracy of 100% and 88.26% for simple and composite activities, respectively.