Results from the Heinrich Event Intercomparison (HEINO) topic of the Ice-Sheet Model Intercomparison Project (ISMIP) are presented. ISMIP HEINO was designed to explore internal large-scale ice-sheet instabilities in different contemporary ice-sheet models. These instabilities are of interest because they are a possible cause of Heinrich events. A simplified geometry experiment reproduces the main characteristics of the Laurentide ice sheet, including the sedimented region over Hudson Bay and Hudson Strait. The model experiments include a standard run plus seven variations. Nine dynamic/thermodynamic ice-sheet models were investigated; one of these models contains a combination of the shallow-shelf (SSA) and shallow-ice approximation (SIA), while the remaining eight models are of SIA type only. Seven models, including the SIA–SSA model, exhibit oscillatory surges with a period of ∼1000 years for a broad range of parameters, while two models remain in a permanent state of streaming for most parameter settings. In a number of models, the oscillations disappear for high surface temperatures, strong snowfall and small sediment sliding parameters. In turn, low surface temperatures and low snowfall are favourable for the ice-surge cycles. We conclude that further improvement of ice-sheet models is crucial for adequate, robust simulations of cyclic large-scale instabilities.