A nonlinear modal analysis is proposed to describe the dynamic behavior of nonlinear multi-degree-of-freedom systems. The solution is based upon the nonlinear mode superposition approach. The calculation of nonlinear natural frequencies and nonlinear normal modes of nonlinear structures obtained by using the single nonlinear mode approach is reviewed and compared to that obtained implicitly by the proposed approximation based upon the equivalent linearization approach. The aim of this work is to obtain a simple and rapid stationary solution which can be applied to real cases of large structures having nonlinear stiffness. In the experimental purpose, the new identification method of nonlinear modes obtained from forced responses is introduced. This approach is particularly important for large order systems for which a truncation of infinite modal coordinates to only a few lower modal coordinates can considerably reduce computational time. Some examples including experimental simulation have been introduced to illustrate the efficiency, the accuracy and the advantages of the proposed methods.