The correct prediction of shear stresses in lubricants applied to concentrated rolling/sliding contacts has been an issue of intense debate for many years. Traction testers of various kinds such as two-disc roller rigs or ball on disc apparatus have been extensively used in order to obtain experimental data, as well as, more recently, molecular dynamics simulations. Several, partly competing, phenomenological models have been developed to describe the dependence of shear stresses on various parameters. Evidently, the importance lies in the need to predict and reduce friction, or, more accurately, resistance to motion of rolling element bearings in order to increase efficiency of machines and vehicles. Also, it plays a crucial role in design and performance of traction drives. As a prerequisite, experimental data for a wide variety of fluids were obtained from two-disc roller tests with a wide variation of contact pressures, rolling speeds and slide-to-roll ratios. Following earlier investigations, the amount of slip created by the elastic deformation of the discs was separated from the contribution of the fluids and their rheological properties. In accordance with experiments of Jacobson a threshold pressure in the fluid was identified which marks the onset of a nearly linear relationship between a limiting shear stress and pressure. However, this threshold does not appear to be constant but rather declining with decreasing hydrodynamic film thickness respective of rolling speed, while the slope changes to a lesser extent. When measurements were extended far into the mixed lubrication regime close to the limiting case of boundary lubrication, the shear stress/pressure relationship became quasi-Coulomb with a virtually zero threshold pressure. These results have successfully been used to predict the friction torque of angular contact ball bearings and the traction characteristics in toroidal drives. © IMechE 2012.