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Non-viscous damped structure systems in which the damping forces depend on the past history of velocities via convolution integrals over some kernel functions have been raised in many different subjects. The developed analysis methods of dynamic response for such structure systems are almost limited to the deterministic time-history excitation. There is little research report on the random response of such non-viscous damped systems. The goal of this paper is to develop two methods, i.e., direct frequency response method and iterative method using real modes, to obtain the power spectral density function (PSDF) of non-viscously damped structure systems subjected to stationary stochastic excitation. First, the pseudo excitation method converts the stationary stochastic excitation problem into harmonic excitation problem. Second, the direct frequency response method is derived and proven to get the analytical solution of PSDF. Third, the iterative method using real modes to obtain PSDF matrix is developed based on a harmonic response method. The computational procedure of the iterative method is given in detail. Finally, the random response analyses of two non-viscously damped structure systems, subjected to stationary random excitation, are demonstrated. The results indicate the two methods can achieve the exact solution of PSDF matrix of non-viscously damped structure systems. The iterative method using real modes is more efficient than direct frequency response method.