The current paper is concerned with the investigation of the relationship between the harmonic balance method (HBM) and the non-linear output frequency response function (NOFRF) approach in the analysis of non-linear systems. Both are applied to the Duffing's oscillator to demonstrate their relationships. The results reveal that, if the Volterra series representation of a non-linear system is convergent, the harmonic components calculated by the NOFRFs are a solution of the HBM. Moreover, the simulation studies show that, in the convergent cases, the NOFRF method can give more accurate results for the higher-harmonic components than the HBM. The relationship investigated in the current study between the two methods should help researchers and engineers to understand the HBM and the NOFRF methods.