The Baffin Bay and the Labrador Sea are located between Greenland and Canada. Both basins evolved from Cretaceous to Eocene times. They are linked by the bathymetric high of Davis Strait, which limits the water transport between both basins. The Labrador Sea is an extinct rift system of the early North Atlantic. Oceanic crust has been identified from magnetic spreading anomalies. It is also proposed that the crust of Baffin Bay is oceanic. But no clear magnetic spreading anomalies are detected and therefore the presence of stretched continental crust is also possible. A similar controversy exists on the nature of the Davis Strait crust. Thick oceanic crust as well as continental fragments are debated. The tectonic evolution of the area is an important factor for the role of Davis Strait as a polar gateway in palaeocean models. In 2008 and 2010 research expeditions to the Davis Strait and Baffin Bay were undertaken to collect geophysical data on the tectonic evolution of this area. Here, I present P-wave velocity and density models of a 710-km-long line in southern Baffin Bay and of a 315-km-long line in the central Davis Strait. The models are supported and complemented by seismic reflection and magnetic anomaly data. The models support results of previous studies: southern Baffin Bay is underlain by oceanic crust of 7.5 km thickness on average. The crust is covered by sediments of up to 6 km thickness. Conjugate to breakup volcanics off Baffin Island, we find seaward dipping reflector sequences in the seismic reflection data of the Greenland margin. We conclude, that the opening of southern Baffin Bay was accompanied by volcanism. The Davis Strait is also characterized by volcanism - along most of the profile basalt flows are imaged. The models reveal that the Davis Strait consists mainly of sections of continental crust. These are saparated by a 45-km-wide unit of new igneous or highly intruded, stretched, continental crust. We account this feature to an influence of the early North Atlantic mantle plume. With the new information of our crustal models, I developed a plate kinematic model. Although southern Baffin Bay is underlain by oceanic crust, magnetic spreading anomalies are probably missing due to many fractures. These lead to small scale crustal sections which are shifted to each other. Due to the reorientation of the Greenland plate in the Late Paleocene, compressional forces were compensated in the Davis Strait. These probably resulted first in a deformation within the Ungava Fault Complex (the pre-Eocene plate boundary) and then caused the evolution of a new transform fault, the Hudson Fracture Zone. To estimate at what time a water transport was possible via the Davis Strait and how the Labrador Sea basin evolved, I calculated palaeobathymetry grids. I compiled published and new seismic data with information from drill sites. In a backstripping routine, I calculated the effects of flexual unloading for the lithosphere, of sedimentdecompaction, of global sea-level changes, and of thermal subsidence of the lithosphere. Palaeolocations of the profiles and the age structure of the crust are derived from our recent plate kinematic model. Although the grids are characterized by great uncertainties, we can conclude that the Davis Strait separated the Labrador Sea from the Baffin Bay in pre-Eocene times. We propose that, similar to today, an early West Greenland Current formed a cyclonic circulation in the early Labrador Sea basin since the Paleocene. Our palaeobathymetric reconstruction can be used in palaeocean models and improve palaeoclimate reconstructions.