Oblique random forests (ObRFs) have attracted increasing attention recently. Their popularity is mainly driven by learning oblique hyperplanes instead of expensively searching for axis-aligned hyperplanes in the standard random forest. However, most existing methods are trained in an off-line mode, which assumes that the training data are given as a batch. Efficient dual-incremental learning (DIL) strategies for ObRF have rarely been explored when new inputs from the existing classes or unseen classes come. The goal of this article is to provide an ObRF with DIL capacity to perform classification on-the-fly. First, we propose a batch multiclass ObRF (ObRF-BM) algorithm by using a broad learning system and a multi-to-binary method to obtain an optimal oblique hyperplane in a higher dimensional space and then separate the samples into two supervised clusters at each node, which provides the basis for the following incremental learning strategy. Then, the DIL strategy for ObRF-BM, termed ObRF-DIL, is developed by analytically updating the parameters of all nodes on the classification route of the increment of input samples and the increment of input classes so that the ObRF-BM model can be effectively updated without laborious retraining from scratch. Experimental results using several public data sets demonstrate the superiority of the proposed approach in comparison with several state-of-the-art methods.