This paper is concerned with the nonlinear stability of two-dimensional quasigeostrophic motions in atmosphere and oceans. By using an accurate a prior estimate method, some nonlinear criteria are obtained, which can be applied to the perturbations of both the initial conditions and parameters in the models rather than those of the former only. It is also shown that the conservation of mass plays an important role in presenting some better criteria of nonlinear stability. Some steady flows are presented, which can be claimed to be nonlinear stable by only the criteria established in this paper. The method of Shepherd (1988) on bounding the finite-amplitude growth of disturbances to unstable flows is also developed by considering the perturbation of parameters.