A device for truing and regulating the tension of spoked running wheels includes a support device for stationarily clamping the hub of the running wheel, a measuring device for determining the lateral and top eccentricity of the rim, a device for fixing a motor-driven nipple wrench to the spoke nipple, a device for manually adjusting spoke tension. The hub of the running wheel is clamped for measuring symmetrical to the axial radial plane; both lateral and top eccentricity and rim anomalies on the same radial rim segment can be read out directly and electronically with or without the tires fitted. A wrench can be installed in existing devices; and is suitable for manual and motor-driven applications.