Nine deep wells (TD from 4793 to 5903 m) drilled with Jurassic syn-rift targets in the Danish-Norwegian Central Graben show abnormal vitrinite reflectance (VR) profiles. They all penetrated thick (up to 950 m) post-rift Upper Cretaceous chalk sections and about 3000 m of Cenozoic mudstone-dominated sediments. The penetrated strata in the wells are further characterised by high fluid pressures (overpressure) in the thick sections of Upper Jurassic-lowermost Cretaceous mudstones forming the principal source rocks in the area. The overpressure in the Jurassic sandstone reservoir target may attain a value of about 50 MPa. The wells display overall the same VR profiles characterised by three VR segments: (i) a more or less well-defined increase in VR through the Cenozoic to the top of the Upper Cretaceous chalk, (ii) an interpolated lower VR gradient through the chalk section, and (iii) a likewise well-defined increase in VR from the base of the chalk and through the Upper Jurassic-lowermost Cretaceous mudstones, but with a higher gradient than determined for the Cenozoic strata. The VR values at the top of the source rock section are much lower than expected indicating that maturation is significantly retarded. The lower VIZ values are determined by two factors: (i) the high thermal conductivity of chalk accounts for the interpolated lower VR gradients in the thick chalk sections, while the higher VR gradients and the higher geothermal gradients in the Upper Jurassic-lowermost Cretaceous source rock mudstones agree with the low thermal conductivity of mudstone, and (ii) the thick sections of overpressured mudstones serve as insulator for the overlying chalk and retard source rock maturation as excessive pressure can prevent liquid and gaseous generation products to escape the source rock and thereby preventing the condensation and reorganisation of the organic matter, which is necessary to increase maturity. Indirect evidence of the effect of excessive pressure comes from maturity modelling of the measured VR values in the Danish Hejre-1 well using the Easy%R-o and PresR(o) models, the latter incorporating pressure. Calibrated with measured present day pressures the PresR(o) model is able to predict the measured VR values, and thus the maturity gradient, and predicts the source rock interval in the well to be in the middle of the oil window even at a depth of 5000 m. Hence, as a consequence of the irregular maturity trends the Upper Jurassic - lowermost Cretaceous source rocks are of lower thermal maturity than expected and if the top of the oil window is set at a VR of 0.6%R-o the decreased maturation results in a downward displacement of the top of the oil window of up to approximately 200-350 m. (C) 2012 Elsevier B.V. All rights reserved.