Over the last decade, nonlinear phenomena in low-temperature fuel cells as well as high-temperature fuel cells have been reported in the open literature. Experimental and theoretical studies found multiple steady states as well as periodic oscillations. The present article gives an overview of publications on this subject. Instead of sorting the analyses according to the types of fuel cells, this work used the source of the nonlinearity for classification. In the first part of the contribution, a very simple prototype fuel cell model is introduced. The model helps to give a qualitative explanation of the majority of nonlinear effects reported in literature. It is further used to identify potential sources of nonlinear behavior in reaction kinetics, membrane properties, and mass transport mechanisms. A classification scheme that is based on types of negative differential resistance (NDR) and was originally introduced by K. Krischer in Modern Aspects of Electrochemistry (Vol. 32, p. 1, Plenum Press, 1999) for electrochemical systems is applied to fuel cells. The second part of the work classifies the findings from literature according to their NDR type. Instabilities resulting not from electrochemistry but from other mechanisms such as water formation and reactant starvation are also discussed.