Two-dimensional equilibrium boundary-layer flows were investigated in an open water channel with a width/depth ratio of 6 for a smooth bed of 0.16 mm quartz grains (d50) and compared with those of an immobile smooth cemented bed with the same sand roughness. For flows at Reynolds numbers between 20,000, representing onset of erosion, and 28,000, before appearance of rhomboid ripples, quartz grains rolled over an otherwise smooth sand bed with a density of ≤40 grains cm−1 s−1. Then the universal law of the wall, as obtained for the fixed, smooth sand bed, could not be confirmed by the data. Instead, (1) a logarithmic layer was found that extended further into the wake region and had a reduced value of von Karman's constant κ = 0.32 ± 0.04, (2) the friction diagram indicated Reynolds number dependent drag reduction, and (3) the logarithmic layer extended down to the top of the rolling grains at ReU >25,000. These results are interpreted as a new class of wall-bounded shear flow with different momentum transfer processes and a velocity-defect law throughout the flow down to the top of the rolling grains. Some conclusions are discussed for sedimentological and engineering problems in which this type of flow is the rule rather than the exception.