In the present study, a new concept known as the Associated Output Frequency Response Function (AOFRF) is introduced to facilitate the analysis of the effects of both linear and nonlinear characteristic parameters on the output frequency responses of nonlinear systems. Based on the AOFRF concept, the study has shown, for the first time, that the output frequency responses of a wide class of nonlinear systems that are described by the NARX (Nonlinear Auto Regressive with eXogenous input) model can be represented by a polynomial function of both the system linear and nonlinear characteristic parameters of interests to the system analysis. Moreover, an efficient algorithm is derived to determine the structure and coefficients of the AOFRF based representation for system output frequency responses. Finally, a case study is provided to demonstrate the effectiveness and advantages of the new AOFRF based representation and the implication of the result to the analysis and design of nonlinear systems in the frequency domain. (C) 2018 Elsevier Ltd. All rights reserved.