Nowadays scientists are working on removing the destructive effect of vibration phenomenon that has unfavorable effect on industrial devices which can be harmful or can destroy them. In vibration study, linear model of the system can be incorrect or misleading. Nonlinear characteristics in a mechanical system may cause vibration behaviors that cannot be seen or predicted when the system modeled linearly. In first part of this thesis non-linear vibration of a 2D-O-F system consists of main system and absorber have been studied at simultaneous secondary and internal resonance and simultaneous primary and internal resonance under external excitation. Then the main system on a mechanical isolator and mentioned resonance states was studied. The studying system with mass, spring and damper were simulated and their springs with cubic nonlinearity was considered. External excitation is applied to the main system. By solving equation of motion using perturbation multiple time scale method, the frequency response equations considering the main system and absorber amplitude was achieved. After that, effects of parameters of the system on the amplitude of main system were investigated. Keywords: Nonlinear vibration, external excitations, primary and secondary resonant, multiple time scale method