Abstract: The nonlinear dynamic systems exhibit particular behaviors when subjected to combined deterministic and stochastic ex? citation. A semi-analytical method for calculating the nonstationary response of a fractional nonlinear oscillator subjected to com ? bined excitation is proposed. Representing the system response as a sum of a deterministic component and zero-mean stochastic component leads to two equivalent sub-equations for the differential equation of motion. The time-varying harmonic balance meth? od is used for the nonstationary solution of the deterministic differential sub-equation， while the statistical linearization method is utilized for obtaining an equivalent linear substitution for the stochastic sub-equation. A semi-analytical solution of the equivalent lin? ear equation is obtained by the Prony-SS and Laplace transform technique. The unknown deterministic/stochastic response compo? nents are obtained by solving the derived nonlinear algebraic equations simultaneously. Monte Carlo simulations demonstrate the applicability and accuracy of this method.