Broad Learning System proposed recently Ill demonstrates efficient and effective learning capability. Moreover, fast incremental learning algorithms are developed in broad expansions without an entire retraining of the whole model. Compared with the systems in deep structure, the inspired system provides competitive results in classification. In this paper, the broad learning algorithms and incremental learning algorithms are applied to commonly used neural networks, such as radial basis function neural networks (RBF) and hierarchical extremal learning machine (H-ELM). For RBF, the resulting models, called BLS-RBF, are established by regarding the radial basis function as the mapping in the enhancement nodes, and additional enhancement nodes are added if the network needs expansion widely. For H-ELM, the established model, is developed for the incremental extension of multilayer structure. The developed BLS models and algorithms are very effective and efficient in classification. Finally, experimental results are presented.