Measurements made with satellite-tracked buoys drogued in different layers between the sea surface and 30-m depth under homogeneous winter conditions in the North Sea allow analysis of the Ekman currents under a large variety of wind conditions. The experiment lasted from November 20, 1991, until February 29, 1992. The first 4 weeks of this period, during which the buoys stayed close together, are used to determine the Ekman stresses. The total current field is a superposition of barotropic currents due to sea level variations and Ekman currents. The classical Ekman theory is not able to describe properly the observed deflection of the currents to the right of the wind direction and their decay with depth. This deflection is 10¿ near the sea surface and increases to approximately 50¿ in 25-m depth. The relation between wind stress and the stress field in the interior of the water is given by a tensor, which describes the rotation and the variation of the stress with increasing depth. The concept of eddy viscosity is applicable, if a viscosity tensor is used to relate stress and vertical shear. The viscosity tensor is a function of the vertical coordinate only and is independent from the wind stress. It shows maximum values in 15- to 20-m depth and may be due to Langmuir circulation cells. Further studies are needed to determine the physics of this tensor. Its magnitude in the interior of the mixed layer exceeds 1000 cgs units. Consequently, Ekman currents are weak and may not be the dominant currents within the mixed layer. ¿ American Geophysical Union 1993