Medical imaging is a central part of clinical diagnosis and treatment guidance. Machine learning has increasingly gained relevance because it captures features of disease and treatment response that are relevant for therapeutic decision-making. In clinical practice, the continuous progress of image acquisition technology or diagnostic procedures, the diversity of scanners, and evolving imaging protocols hamper the utility of machine learning, as prediction accuracy on new data deteriorates, or models become outdated due to these domain shifts. We propose a continual learning approach to deal with such domain shifts occurring at unknown time points. We adapt models to emerging variations in a continuous data stream while counteracting catastrophic forgetting. A dynamic memory enables rehearsal on a subset of diverse training data to mitigate forgetting while enabling models to expand to new domains. The technique balances memory by detecting pseudo-domains, representing different style clusters within the data stream. Evaluation of two different tasks, cardiac segmentation in magnetic resonance imaging and lung nodule detection in computed tomography, demonstrate a consistent advantage of the method., In clinical practice, the continuous progress of image acquisition technology or diagnostic procedures and evolving imaging protocols hamper the utility of machine learning, as prediction accuracy on new data deteriorates. Here, the authors propose a continual learning approach to deal with such domain shifts occurring at unknown time points.