Permian rifting and magmatism are widely documented across NW Europe. The different Permian basins often display contrasting structural styles and evolved in lithospheric domains with contrasting past evolution and contrasting thermotectonic ages. In particular, the Oslo Graben and the northern North Sea rift initiated in close areas of northern Europe. The Oslo Graben evolved in the cold and stable Precambrian lithosphere of Fennoscandia, whereas the northern North Sea rift took birth in freshly reworked Caledonian lithosphere. Huge volumes of magmatic rocks characterize the relatively narrow Oslo Graben. In contrast, little magmatism is documented for the wide northern North Sea rift. Differences in timing between both rifts are inferred but still debated. We present numerical thermomechanical models along a lithospheric E-W section that involves both the Oslo Graben and the northern North Sea area. Because the modeled section crosses the boundary between Caledonian and Proterozoic provinces, thermal and compositional heterogeneities are considered. As is suggested by various geophysical data sets, we also consider lithospheric thickness heterogeneities in the Precambrian lithosphere. Modeling results suggest that the northern North Sea was on top of "weak" lithosphere very sensitive to far-field stresses. Consequently, we suggest that rifting in the northern North Sea began as early as regional extension was effective (i.e., Late Carboniferous-Early Permian) and does not postdate the Oslo Graben as it is commonly assumed. Rifting in the "strong" Precambrian lithosphere is unexpected. Modeling results suggest that a pre-existing lithospheric thickness contrast within the Fennoscandian lithosphere favored rifting in the Oslo Graben.