This paper studies undamped oscillations of fractional-order Duffing system. Stability theorems for fractional order systems are used to determine the characteristic polynomial of the system in order to find the parametric ranges for undamped oscillations in this system. We also derive relations for estimating the frequency and the amplitude of the oscillations in this system using a describing function method. Finally numerical simulation results are provided to justify the analysis. HighlightsUndamped oscillations of fractional Duffing system is investigated.Parameter region is found using stability theorems.Frequency and amplitude of the limit cycle are estimated using a describing function method.Results are verified using numerical simulations in time domain.