The numerical treatment of the grounding line in dynamic ice-sheet models is crucial because it determines the extent the grounded ice sheet will attain when moving over terrain lying below sea level. The marine ice-sheet problem arises because the grounding zone constitutes the transition between two well-defined ice-deformation regimes for floating and grounded ice, respectively. Here we present the results of four different models tested within the framework of the EISMINT Model Intercomparison exercise. This involved a simple downward sloping bedrock plane overlain by an ice sheet/ ice shelf system subjected to impulse sea-level and accumulation variations. It turned out that no consensus could be reached regarding the geometry of the resulting ice sheets, raising fundamental questions about the state of equilibrium and stability of the ice sheet/ ice-shelf junction and the reversibility of the process of grounding-line migration.