Two mathematical models are developed to predict the minimum liquid fluidization velocity, U-lmf, of a bed of solid particles in the presence of a fixed cocurrent gas velocity U-g. Both models start with the Ergun equation for single phase flow through a packed bed and the assumption that the frictional pressure gradient for fluidization supports the buoyed weight of the bed. The Pseudo-Homogeneous Fluid Model assumes that the gas and the liquid together behave as a homogeneous fluid with composite properties while the Gas-Perturbed Liquid Model assumes that full support of the solids is provided by the liquid, the space occupied being perturbed by the presence of the gas. Other theoretical models from the literature are critically discussed. All models require knowledge of the solids-free gas holdup, alpha, at minimum fluidization. The various models in conjunction with alternative empirical equations for alpha from the literature, as well as published empirical equations for U-lmf, are tested against available experimental data in the literature and from our laboratory. For both wettable and non-wettable particles, the Gas-Perturbed Liquid Model, together with the appropriate equation for alpha, shows almost as good agreement with the experimental data as the best empirical equation for U-lmf, and has the advantage of correctly reducing to the Wen-Yu equation for minimum two-phase fluidization as U-g goes to zero.