ABSTRACT: The nonlinear approach of quantum mechanics is continuously an important direction. In this paper, basic nonlinear operators are proposed and corresponding Heisenberg equation was obtained. Then the present applied superposition principle is developed to the general nonlinear form. The quantum commutation and anticommutation belong to F and . This theory may include the renormalization, which is the correction of Feynman rules of curved closed loops. We think the interaction equations must be nonlinear. Many theories, models and phenomena are all nonlinear, for instance, soliton, nonabelian gauge field, and the bag model, etc. The superluminal entangled state, which relates the nonlocal quantum teleportation and nonlinearity, should be a new fifth interaction. Moreover, the nonlinear effects exist possibly for various interactions, for single particle, for high energy, and for small space-time, etc. The relations among nonlinear theory and electroweak unified theory, and QCD, and CP nonconservation, etc., are expounded. Finally, some known and possible tests are discussed. The nonlinear theory relates the possible decrease of entropy in isolated system.