Uncertainties in dynamic systems are common in real applications, provoking substantial troubles in any control realization and being a source of instability or poor performance for tracking or regulation problems. Considerable research efforts had been undertaken on control designing for uncertain nonlinear dynamic systems over the last thirty years. There are several approaches to design and construct a control in this situation. Among them, the more effective are the Artificial Neural Networks (ANN) and the Sliding Mode (SM) technique with all possible variants within (Integral Sliding Mode, Higher Order Sliding Mode, etc.). Such combination seems to be very promising ,  because it provides a new instrument for identification, state estimation and control of many classes of uncertain systems affected by external perturbations. This chapter deals with the realization of this idea and suggests an adaptive control designing based on both Differential Neural Network Observation and High Order Sliding Mode Technique. Below this approach is referred to as High Order Sliding Mode Neural Control (HOSMNC).