With the increasing adoption of teledermatology, there is a need to improve the automatic organization of medical records, being dermatological image modality a key filter in this process. Although there has been considerable effort in the classification of medical imaging modalities, this has not been in the field of dermatology. Moreover, as various devices are used in teledermatological consultations, image acquisition conditions may differ. In this work, two models (VGG-16 and MobileNetV2) were used to classify dermatological images from the Portuguese National Health System according to their modality. Afterwards, four incremental learning strategies were applied to these models, namely naive, elastic weight consolidation, averaged gradient episodic memory, and experience replay, enabling their adaptation to new conditions while preserving previously acquired knowledge. The evaluation considered catastrophic forgetting, accuracy, and computational cost. The MobileNetV2 trained with the experience replay strategy, with 500 images in memory, achieved a global accuracy of 86.04% with only 0.0344 of forgetting, which is 6.98% less than the second-best strategy. Regarding efficiency, this strategy took 56 s per epoch longer than the baseline and required, on average, 4554 megabytes of RAM during training. Promising results were achieved, proving the effectiveness of the proposed approach.