The paper is devoted to nonlinear optimal control problem. A strategy for optimal nonlinear feedback control of linear and nonlinear structures under random loading is proposed based on stochastic averaging method for quasi-Hamiltonian systems and on the stochastic dynamic programming principle. The optimal control forces are obtained by solving the equations for ergodic control problem and for an optimal control problem with some cost function. These equations are solved using the stochastic averaging method. The authors present examples to show the advantages of the proposed control strategy (Duffing oscillator under white and non-white wide-band random excitations). It should be noticed that the responses of uncontrolled and controlled systems to optimal control forces can be predicted analytically.