It is the final purpose of the study to establish a method of analysis on general nonlinear behaviors of plates……material and geometrical nonlinearitis…. In this paper, these nonlinear behaviors are separately investigated. For the behaviors of plates under incremental loading, the fundamental equilibrium equations are developed for each step of load increment which is sill of nonlinear form with respect to the resulting deformations. To eliminate difficulties in solving the above equations, higher order terms in the equations are neglected and linear fundamental equations are obtained, since the increment of loads at each step is to be kept so small that the effect of the higher order terms is estimated negligibly small on the results. Based on these linear equations, analytical methods are proposed for each nonlinear behavior, and several examples are solved by the methods with the aid of Galarkin's method. The examples for material nonlinearlity are on elastic-plastic behavior of simply supported rectangular plates under uniform pressure and for geometrical nonlineality large deformation of simply supported rectangular plates subjected to compression, and shear at the edges with consideration of the effect of initial imperfection. The results of the analysis verified the usefulness of the methods and assured the possibility of analysis on general nonlinear behaviors of plates.