Conductivity-temperature-depth transects across the Greenland Sea and Fram Strait provide geostrophic shear velocity profiles, which were absolutely referenced using the simultaneous measurements from a vessel-mounted acoustic Doppler current profiler. The measurements are performed mainly in 1997, with supplements in 1998, 1995, and 1994. The observations confirm that all currents within the area have a strong barotropic component so that calculations based on the geostrophic method underestimate the transports considerably. Particulars for the transports of mass and heat are given for all individual and total water masses in the area. Meanders and eddies on horizontal scales between 20 and 70 km affect the total transport in the West Spitsbergen Current significantly. The Atlantic Water transports range between 2 and 7 Sv, mainly dominated by the cross-sectional area occupied by this water mass. The total northward heat transport across 75¿N is estimated as 54.7 TW and across 79¿40'N as 42 TW in September 1997.