The 2D-finite-difference code TEMISPACK is used to discuss the history of hydrocarbon (HC) generation, expulsion and migration along a 160 km long transect across the Northern Viking Graben. In the first section, HC generation is discussed based on hypotheses on the crustal heat flow; a kinetic model is used to calculate the maturity. Observations are shown to be consistent with a 67 mW m-2 heat flow, possibly 60 mW m-2 in the graben axis. The precision of the calibrated heat flow is not more than 10%, which results in an uncertainty of the timing of HC generation of 5-10 Ma. The development of overpressures, observed today in the deep Jurassic reservoirs is shown to be essentially controlled by compaction, with a minor contribution due to gas generation; the model also shows that faults related to the Jurassic rifting are most certainly impermeable. In the second section, the previous overpressures and maturity reconstructions form the framework in which expulsion and migration of HC are modelled, based on the two-phase (water, hydrocarbon) Darcy law. The computation explains the filling of the tilted blocks located in the Tampen Spur zone as well as the presence of gas at Troll. A sensitivity analysis shows the importance of poorly constrained parameters such as the relative permeability curves, capillary pressures, or the properties of the petroleum fluids.