In nonlinear structural vibration analysis, using the linear modeling may lead to wrong results. To accurately predict vibration behavior of structures, a complete mathematical modeling is necessary. Most systems that are analyzed by using linear mathematical models are in fact nonlinear systems. Nonlinear characteristics of a system may cause behaviors in the response that linear modeling does not have the ability to predict and explain. In this thesis, the nonlinear vibrations and stability of a two degree of freedom system consisting of the main system and an absorber is studied under external excitation. The cases of simultaneous secondary and internal resonances, and simultaneous primary and internal resonances are considered for the analysis. The absorber is used to control the main system vibrations when subjected to an external excitation force. The system springs and dampers have both linear and cubic nonlinear terms. The governing equations of motion of the system are derived using the Newton's second law. To solve the equations, the method of multiple time scale (MTS) which is an approximate method suitable for solving nonlinear differential equations have been used. By separating the secular terms, the frequency response equations of the system are obtained. The effects of linear and nonlinear parameters of the system on the amplitude of the main system is investigated. Stability analysis of the responses is performed by the method of Andronov and Vitt and the saddle-node bifurcation points are detected. Also the domain of the detuning parameter related to the three response zone is determined. If the detuning parameter is selected in this domain, the jump phenomenon occures in the response. Moreover, the possibility of existence of bifurcation phenomenon in the response is studied. In this way, at first the system equations of motion were expressed in dimensionless form. Then, by defining the state variables, the equations are expressed in state space form. These equations were solved by using the fourth-order runge-kutta method in Matlab software. To perform bifurcation analysis, a bifurcation parameter known as control parameter should be choosen. In this analysis dimensionless excitation frequency is determined as the control parameter. Bifurcation diagram is drawn in order to detect periodic and chaotic responses. The Poincaré map diagram, phase-plane diagram and time response are used at different control parameter vlues to distinguish periodic, quasi-periodic and chaotic motions. By using these diagrams, the system parameters can be selected such that the quasi-periodic and chaotic responses do not occure. Keywords: Nonlinear vibrations, Vibration absorber, Multiple time scale method, Superharmonic resonance, Bifurcation.