In the field of earth observation (EO), continual learning (CL) algorithms have been proposed to deal with large datasets by decomposing them into several subsets and processing them incrementally. The majority of these algorithms assume that data are, first, coming from a single source, and second, fully labeled. Real-world EO datasets are instead characterized by a large heterogeneity (e.g., coming from aerial, satellite, or drone scenarios), and for the most part they are unlabeled, meaning they can be fully exploited only through the emerging self-supervised learning (SSL) paradigm. For these reasons, in this article, we present a new algorithm for merging SSL and CL for remote sensing applications that we call continual Barlow twins. It combines the advantages of one of the simplest self-supervision techniques, i.e., Barlow twins, with the elastic weight consolidation method to avoid catastrophic forgetting. In addition, we evaluate the proposed continual SSL approach on a highly heterogeneous EO dataset, showing the effectiveness of this strategy on a novel combination of three almost non-overlapping domains datasets (airborne Potsdam, satellite US3D, and drone unmanned aerial vehicle semantic segmentation dataset), on a crucial downstream task in EO, i.e., semantic segmentation. Encouraging results show the superiority of SSL in this setting, and the effectiveness of creating an incremental effective pretrained feature extractor, based on ResNet50, without the need of relying on the complete availability of all the data, with a valuable saving of time and resources.