||The empirical mode decomposition (EMD) method is well-known for its ability to decompose a multi-component signal into a set of nonlinear intrinsic mode functions (IMFs). This method provides an effective and robust approach for decomposing nonlinear and non-stationary signals. However, the IMF components do not automatically guarantee a well-defined physical meaning hence, it is necessary to validate the IMF components carefully prior to any further processing and interpretation. In this study, EMD-based methods are developed to identify properties of nonlinear multi-degree-of-freedom (MDOF) structures. It is first shown that the EMD results of the displacement responses of a nonlinear non-hysteretic structure are numerical close to the nonlinear normal mode (NNM) responses while the EMD results of the displacement responses of a hysteretic structure are numerically close to nonlinear modal responses and offsets. Based on this agreement, two EMD-based identification techniques are developed to estimate the parameters of nonlinear non-hysteretic and hysteretic structures. The results of both numerical and experimental studies show that the two proposed EMD-based methods provide possible means for obtaining nonlinear properties in a structure. It is known that the computational cost may be too expensive for the identification of full-scaled or detailed models of structures. Since the IMF components can be used as modal coordinates as well as provide estimates for responses at unmeasured locations if the mode shapes of the structure are known, the EMD-based technique is proposed for identifying and quantifying nonlinear behavior in damaged structures using incomplete measurement. Since the identification is performed in the modal domain, the proposed method is very efficient. Two procedures are developed for identifying nonlinear damages in the form of non-hysteresis and hysteresis in a structure. Both numerical and experimental studies show that the proposed method can be reasonably identified the type and physical location(s) of nonlinearity in a structure.