A fluid friction clutch, suitable especially for a cooling fan of an internal combustion engine, has a shear gap of substantially serpentine form seen in axial longitudinal section, which is formed by concentric annular ribs. The ribs of the two parts which form the shear gap engage in each case in concentric annular grooves between radially adjacent ribs of the other part. The ribs have conical ring flanks with a flank angle preferably of 30.degree. and terminate in a flat end face perpendicular to the rotation axis. The groove bottom opposite to this end face has a rounded cross section and is spaced from the end face by a distance about equal to 1.2 to 1.4 times the width of the shear gap between opposed rib flanks. Because of this geometry, the fluid friction clutch has a very great torque transmission capacity with small dimensions and reacts very rapidly to variations of state. The configuration of the ribs and channels guarantees an optimum conductance of heat and affords only a relatively slight flow resistance to the shear fluid.