Abstarct: Dynamic sliding mode control (DSMC) of nonlinear systems using neural networks is proposed. In DSMC the chattering is removed due to the integrator which is placed before the input control signal of the plant. However, in DSMC the augmented system is one dimension bigger than the actual system and then, the plant model should be completely known. To solve this problem, we suggest two online neural networks to identify and to obtain a model for the unknown nonlinear system. In the first approach, the neural network training law is baxsed on the available system states and the bound of observer error is not proved to converge to zero. The advantageous of the second training law is only using of the system output and the observer error is converges to zero baxsed on the Lyapunov stability theorem. To compare result, Dynamic Sliding Mode Control (DSMC) using sliding mode observer is proposed. This approach caused control system absolutely robustness rather to noises and disturbances. This approach proved using Lyapunov stability theorem, too. To verify these approaches Duffing-Holmes chaotic systems (DHC) is used.