For the identification problem of Multi-Degree of Freedom (MDOF) nonlinear systems, the dynamic parametrical model of a nonlinear system is presented based on the Non-linear Autoregressive with Exogenous inputs (NARX) model and considering the physical design parameters of interest of the systems. Firstly, the NARX model is established under the condition that different design parameters are considered, where each of the established NARX model is only related to the input and output data. These models are then unified to a common structure by using the proposed Extended Forward Orthogonal Regression (EFOR) algorithm. Secondly, the relationship between the coefficients of each unified NARX model and the corresponding physical design parameters are built in order to obtain the dynamic parametrical model of the MDOF nonlinear system. Furthermore, a Single Input Single Output (SISO) 2DOF nonlinear system is taken for a case study to clarify the modeling process of dynamic parametrical model in detail by using the results of numerical simulation. Finally, a cantilever beam with nonlinear coating damper is employed for an experimental validation of the proposed modeling method. The dynamic parametrical model of the beam is established to reflect its dynamic characteristics. The results indicate that the dynamic parametrical model of the nonlinear systems can accurately predict the response of the nonlinear systems, which provides the theoretical basis for the analysis and design of nonlinear systems.