Real-time monitoring of human behaviours, especially in e-Health applications, has been an active area of research in the past decades. On top of IoT-based sensing environments, anomaly detection algorithms have been proposed for the early detection of abnormalities. Gradual change procedures, commonly referred to as drift anomalies, have received much less attention in the literature because they represent a much more challenging scenario than sudden temporary changes (point anomalies). In this paper, we propose, for the first time, a fully unsupervised real-time drift detection algorithm named DynAmo, which can identify drift periods as they are happening. DynAmo comprises a dynamic clustering component to capture the overall trends of monitored behaviours and a trajectory generation component, which extracts features from the densest cluster centroids. Finally, we apply an ensemble of divergence tests on sliding reference and detection windows to detect drift periods in the behavioural sequence.