Nonlinear systems with convergent Volterra series representations are considered. New definitions of stability and stabilizability and the H-infinity norm for nonlinear systems will be presented via the Laplace transform of the corresponding Volterra kernel. Second-order and bilinear systems are used as examples to deal with the stability in detail. In particular the H-infinity norm for some bilinear systems and the boundary of the H-infinity norm for nonlinear separable systems are given explicitly. Finally, the stabilizability of the second-order system via dynamic output feedback is analysed.