This is an extension to a previous study of the Wahl–Fischer torsional instability problem (Infante and Doughty, “An Old Problem Reconsidered: The Wahl–Fischer Torsional Instability Problem”, J. Appl. Mech. Trans. ASME, 2020, 87(10), p. 101004). There, we provided a mathematical explanation of the reasons for the existence of torsional oscillations observed in numerical simulations and in actual mechanical devices such as the exhaust fan system studied by Wahl and Fischer. That explanation was mostly based on linear analysis. This paper presents an additional mathematical explanation of the nature and form of the large self-excited oscillations, due to the strongly nonlinear nature of the system and the large amplitude of these oscillations. Because the oscillations are large, their study requires the use of nonlinear methods.