Abstract: Most of Continual Learning (CL) methods push the limit of supervised learning settings, where an agent is expected to learn new labeled tasks and not forget previous knowledge. However, these settings are not well aligned with real-life scenarios, where a learning agent has access to a vast amount of unlabeled data encompassing both novel (entirely unlabeled) classes and examples from known classes. Drawing inspiration from Generalized Category Discovery (GCD), we introduce a novel framework that relaxes this assumption. Precisely, in any task, we allow for the existence of novel and known classes, and one must use continual version of unsupervised learning methods to discover them. We call this setting Generalized Continual Category Discovery (GCCD). It unifies CL and GCD, bridging the gap between synthetic benchmarks and real-life scenarios. With a series of experiments, we present that existing methods fail to accumulate knowledge from subsequent tasks in which unlabeled samples of novel classes are present. In light of these limitations, we propose a method that incorporates both supervised and unsupervised signals and mitigates the forgetting through the use of centroid adaptation. Our method surpasses strong CL methods adopted for GCD techniques and presents a superior representation learning performance.