Under-expanded jets which are discharged from an orifice or a nozzle have long been subject of researches for aeronautical and mechanical applications. Provided that the jet pressure ratio and nozzle configuration are known, the major features of the steady jet are now well known. However, the jet pressure ratio is often varied even during the process in many practical applications. Many questions remain unanswered with regard to how the supersonic jet responds to the transient process of the pressure ratio and whether the steady jet data for a specific pressure ratio can still bear the same during the transient process of pressure ratio. In the present study, the hysteric phenomenon of under-expanded jets has been investigated with the help of computational fluid dynamics methods. The under-expanded jets of both dry and moist air have been employed to investigate the transient processes of the pressure ratio. The effects of nonequilibrium condensation occurring in the under-expanded moist air jets are explored on the hysteresis phenomenon. It is known that under-expanded air jet produced during the startup transient of jet behaves differently from the shutdown transient process, leading to the hysteric phenomenon of under-expanded jet. It is also known that the moist air jet reduces the hysteric phenomenon, compared with the dry air jet, and that non-equilibrium condensation which occurs in the under-expanded moist air jet is responsible for these findings.