The NE Atlantic Ocean opened progressively between Greenland and NW Europe during the Cenozoic. Seafloor spreading occurred along three ridge systems: the Reykjanes Ridge south of Iceland, the Mohns Ridge north of the Jan Mayen Fracture Zone (JMFZ), and the Aegir and Kolbeinsey Ridges between Iceland and the JMFZ. At the same time, compressional structures developed along the continental margin of NW Europe. We investigate how these compressional structures may have resulted from variations in the amount and direction of seafloor spreading along the ridge system. Assuming that Greenland is rigid and stationary, we have used a least squares method of palinspastic restoration to calculate differences in direction and rate of spreading along the Reykjanes, Kolbeinsey/Aegir and Mohns Ridges. The restoration generates relative rotations and displacements between the oceanic segments and predicts two main periods of left-lateral strike slip along the main oceanic fracture zones: (1) early Eocene to late Oligocene, along the Faeroe Fracture Zone and (2) late Eocene to early Oligocene and during the Miocene, along the JMFZ. Such left-lateral motion and relative rotation between the oceanic segments are compatible with the development of inversion structures on the Faeroe-Rockall Plateau and Norwegian Margin at those times and probably with the initiation of the Fugløy Ridge in the Faeroe-Shetland Basin during the Eocene and Oligocene. The Iceland Mantle Plume appears to have been in a position to generate differential seafloor spreading along the NE Atlantic and resulting deformation of the European margin.