Many practical problems should be described by nonlinear Markov jump systems involving both continuous and discrete variables. In this paper, the stationary response of stochastically excited singledegreeoffreedom (strongly) nonlinear system with Markovian jump parameters is studied. Firstly, the averaged It? differential equation with Markovian jump is derived based on the stochastic averaging method. Then, according to the Markovian jump principle, the finite set of (FokkerPlanckKolmogorov) FPK equations are formulated. The FPK equations coupled with each other through the absorptive terms and reductive terms. The stationary response and its statistics of the Markovian jump system can be obtained by solving the FPK equations numerically. Finally, as an example, the responses of a Markovian jump Duffing oscillator subjected to Gaussian white noise are studied. Numerical results show that the stationary response of the jump system can be regard as a weighted sum of the responses of nojump system, and the weighted value is determined by the jump rules.