To overcome the inefficiency of incremental learning for hyperspectral remote sensing images, we propose a binary detection theory-sequential minimal optimization (BDT-SMO) nonclass-incremental learning algorithm based on hull vectors and Karush-Kuhn-Tucker conditions (called HK-BDT-SMO). This method can improve the accuracy and efficiency of BDT-SMO nonclass-incremental learning for fused hyperspectral images. But HK-BDT-SMO cannot effectively solve class-incremental learning problems (an increase in the number of classes in the newly added sample sets). Therefore, an improved version of HK-BDT-SMO based on hypersphere support vector machine (called HSP-BDT-SMO) is proposed. HSP-BDT-SMO can substantially improve the accuracy, scalability, and stability of HK-BDT-SMO class-incremental learning. Ultimately, HK-BDT-SMO and HSP-BDT-SMO are applied to the classification of land uses with fused hyperspectral images, and the classification results are compared with other incremental learning algorithms to verify their performance. In nonclass-incremental learning, the accuracy of HSP-BDT-SMO and HK-BDT-SMO is approximately the same and is higher than the others, and the former has the best learning speed; while in class-incremental learning, HSP-BDT-SMO has a better accuracy and more continuous stability than the others and the second highest learning speed next to HK-BDT-SMO. Therefore, HK-BDT-SMO and HSP-BDT-SMO are excellent algorithms which are respectively suitable to nonclass and class-incremental learning for fused hyperspectral images.