Considering high order correlations of selected features next to the raw features of input can facilitate target pattern recognition. In artificial intelligence, this is being addressed by Higher Order Neural Networks (HONNs). In general, HONN structures provide superior specifications (e.g. resolving the dilemma of choosing the number of neurons and layers of networks, better fitting specs, quicker, and open-box specificity) to traditional neural networks. This chapter introduces a hybrid structure of higher order neural networks, which can be generally applied in various branches of pattern recognition. Structure, learning algorithm, and network configuration are introduced, and structure is applied either as classifier (where is called HHONC) to different benchmark statistical data sets or as functional behavior approximation (where is called HHONN) to a heat and mass transfer dilemma. In each structure, results are compared with previous studies, which show its superior performance next to other mentioned advantages.