A non-linear reduced-order model has been used to assess the nonlinear stability of labyrinth seals in the case that circumferential variations are neglected. The model numerically solves the integral mass and energy equations of the seal for a prescribed motion until a periodic state is reached. For small vibration amplitudes, the work-per-cycle coincides with the one derived by Corral and Vega (2018, “Conceptual Flutter Analysis of Labyrinth Seals Using Analytical Models. Part I: Theoretical Background", ASME J. Turbomach. 140(10), pp. 121006) and Corral et al. (2021, “Higher-Order Conceptual Model for Seal Flutter”, ASME J. Turbomach. 143(7), pp. 071006), but for large but still realistic vibration amplitudes nonlinearities alter the stability limit. If the seal is supported on the lowpressure side high vibration amplitudes tend to stabilise the seal even more. However, linearly stable seals supported on the high-pressure side can become unstable. Nonlinear effects are significant when the discharge time of the seal is comparable to the vibration period but for high enough frequencies nonlinear effects can be disregarded. This latter limit is the most realistic and therefore it is concluded that nonlinear mechanisms can play a significant role in seal flutter this is not the case for the zero nodal diameter under realistic conditions.