Summary: This paper is concerned with the stochastic stabilization and destabilization of nonlinear differential equations, which, more precisely, further develops the general theory of stochastic stabilization and destabilization that was studied by X. Mao [”Stochastic stabilization and destabilization”, Syst. Control Lett. 23, No.4, 279-290 (1994; Zbl 0820.93071)] and A.D. Appleby,, X. Mao, A. Rodkina [”Stabilization and destabilization of nonlinear differential equations by noise”, IEEE Trans. Autom. Control 53, 683-691 (2008)]. The proposed results are of substantial improvements and reveal the more fundamental principle for stochastic stabilization and destabilization of dynamical systems, which is also verified by applying them to mass-action systems.