It is shown that the well-known and extensively used bubble-point methods, such as the one proposed by Wang and Henke for simulating vapor-liquid multistage distillation problems, can be used efficiently for the simulation of other types of vapor-liquid multistage separation problems, such as absorption and reboiled-absorption processes, even when the thermodynamic properties are a strong function of the composition. Via numerical simulations, it is shown that a robust bubble-point temperature iteration scheme provides convergence stability in the whole bubble-point method. The proposed robust bubble-point temperature iteration scheme is a combination of an equation decoupling method and a simultaneous method. This hybrid bubble-point temperature iteration scheme exploits the reliability of the equation decoupling method, which makes good convergence progress from a poor starting point. However, if the initial point in the bubble-point temperature calculation is good enough, only the equation decoupling method is used, to avoid excessive successive substitution steps when the separation factors are updated. As a consequence of the extension of the bubble-point method to simulate absorption cases, a didiagonal matrix with an off column is generated, when the interstage vapor rates are calculated. An efficient and simple algorithm derived from the Gaussian elimination method to solve the didiagonal matrix with an off column is presented. Results are reported for distillation, absorption, and reboiled-absorption processes, using the Soave-Redlich-Kwong equation of state.