Homogeneous azeotropic distillation processes may exhibit multiple steady states under certain conditions. A methodology has been described for directly capturing all the multiple steady states as well as for generating the bifurcation diagram using the HYSYS process simulator in the steady-state mode. Initial guesses for generating the multiple steady states were based on the infinity/infinity approach of Bekiaris et al. (Ind. Eng. Chem. Res. 1993, 32, 2023) and the behavior of the composition-temperature profiles. The method was tested with different systems, feed locations, and compositions and was extended to nonideal stages using the overall efficiency approach. Conventional inside-out algorithms in the steady-state mode were found to capture the stable steady states only. Using stabilizing control, these algorithms could capture the unstable steady states as well. Their ability to incorporate Murphree efficiencies in the column specifications could, hence, be exploited. Preliminary results on the sustained oscillatory behavior on the higher branch are presented.