This contribution presents the derivation and solution of model equations for a chromatographic system in the presence of multiple fluid phases. While chromatographic models commonly account for adsorption and one single convective phase, macroscopic models for applications in natural reservoirs deal with multiphase flow but usually neglect adsorption effects. This work considers an equilibrium theory model and a lumped kinetic model which account for both multiphase flow and adsorption phenomena. Analytical and numerical solutions of these models are derived and applied to a specific chromatographic system, which was investigated in detail in a companion paper. The analysis of equilibrium theory solutions provides a deep insight in the mathematical and physical implications of two-phase flow and adsorption. The comparison of analytical and numerical solutions validates both models and highlights advantages and drawbacks. The presented model equations and solutions are of considerable interest not only in the context of liquid chromatography but also for several applications involving natural reservoirs.