This paper intends to explore the application of the Reverse Multiple Input Multiple Output (R-MISO) technique in the system identification of nonlinear structural behaviour. This paper introduces two concepts in improving the identification estimates of multiple inputs and nonlinear systems, which is the conditioned spectral estimation technique and the inversion of the frequency response function formulas. In this paper, a linear equation of motion with a nonlinear Duffing oscillator is modelled and tested using this technique in order to model the typical nonlinear stiffness characteristics of materials and their design limit. The results indicate a good fit between the predicted physical parameters and the model properties. The nonlinearities were successfully isolated in a non-iterative procedure and the parameters were correctly identified. Multiple coherency was used as a tool to describe the various contributions of the inputs to the system outputs. © 2019 Published under licence by IOP Publishing Ltd.