A major issue of polymer-electrolyte-membrane (PEM) fuel cell operation is the water management of the cells. This article tries to contribute to an improved understanding of flooding/drying out effects by performing a analysis for a rigorous two-phase PEM fuel cell model. The model is examined by means of a bifurcation analysis. This investigation is performed numerically with parameter continuation methods. The nonlinear behavior is qualified and possible instabilities are detected. A steady state multiplicity is found. The multiplicity is physically explained and the influence of selected fuel cell parameters is investigated. The multiplicity is finally verified in a dynamic simulation. The future work aims at a model reduction of the analyzed fuel cell model to gain a low order model suitable for model-based control strategies.