In this work, a bifurcation analysis of steady states in a multistage agitated contactor (MAC) was conducted for typical gas-liquid processes. A cascade of stirred tank reactors with a backflow was used to model the reactive flow in the MAC, and second-order reaction kinetics was employed to represent typical gas-liquid processes. In the developed model, the effect of temperature on gas solubility was taken into account. The multiplicity behaviour of steady states in such a reactor was investigated using a continuation method. Nonlinearity behaviours such as limit points and Hopf points were detected under various process parameters investigated in this work. A stability analysis was also conducted to determine whether the multiple steady state solutions observed were stable. The results suggested that a medium adiabatic temperature rise and small temperature difference are preferred to avoid system instability in operating such reactors.