The time series of the physical parameters in boiling evaporators with vapor-liquid (V-L) two-phase and vapor-liquid-solid (V-L-S) three-phase external natural circulating flows exhibit nonlinear features. Hence, proper system evolution models may be built from the point of view of nonlinear dynamics. In this work, genetic programming (GP) was utilized to find the nonlinear modeling functions necessary to develop global explicit two-variable iteration models, using wall temperature signals measured from the heated tube in ordinary two-phase and three-phase fluidized bed evaporators. The model predictions agree well with the experimental data of the time series, which means that the models established with GP can adequately describe the dynamic evolution behavior of multi-phase flow boiling systems.