Palaeoseismological investigations are used in many regions of the world to extend back in time the earthquake statistics of historical written or oral records as well as instrumental information. This is very valuable for discussions of earthquake hazard, but it only applies to areas of stable stress regime. Although the intraplate areas of Scandinavia and Greenland have experienced only rather small earthquakes within the human timescale, they serve as a clear warning on the application of palaeoseismology for hazard studies in regions where the stresses have changed. In a small part of Scandinavia, where recent earthquake activity is not significantly different from that of its surroundings, large faults have been discovered and several have been investigated via palaeoseismology. They are interpreted to show the occurrence of large earthquakes about 9000 years ago. Signs of this are coincident landslides as well as liquefaction in loose sediments, which are well dated through varve-counting. In contrast to this the present-day stress release in earthquakes and in surface rock deformations is mainly caused by plate motion. Regional investigations in Scandinavia and Greenland/North America, as well as those included in the World Stress Map Project of the 1990s, have shown compression within the plate, mainly in the direction of absolute plate motion. The ice cap influence has disappeared. So stress reorganization is clearly indicated over the short geological timespan of 9000 years. Into this argument goes the observation from Greenland and Antarctica, that no earthquakes occur under the ice caps. For Scandinavia the argument is that no earthquakes occurred under the ice sheet during the Ice Age, and that the stored stresses were released when the ice sheet melted 9000 years ago. This does emphasize a warning. There are regions of the globe where palaeoseismological investigations can give a fantastic extension of the short-term historical earthquake records. But in some regions stress reorganization has changed this condition.