The main objectives of this study are to examine the random responses of a vibration absorber system with autoparametric coupling in the neighborhood of internal resonance subjected to narrow band random excitation by Gaussian closure scheme and to compare the results with those obtained by Monte Carlo simulation. The Monte Carlo simulation is found to support the main features of the nonlinear modal interaction in the neighborhood of internal resonance conditions. The jump phenomenon of the cantilever mode and saturation phenomenon of the main system are shown to occur if the excitation bandwidth is sufficiently small.