The driven running gear is intended for underslung rail vehicles with at least two articulated body units. It has two individual sets of running gear (2, 2') fitted with steering means (15, 15', 16). These are interconnected to pivot about their horizontal axis beneath the centre of the wheel axles (8, 8') by a link (3), which, at its ends, has transverse bearers (4, 4') to support a body unit to which are secured at least one motor (21, 21') and a brake (23, 23', 24, 24') which drive and brake the running gear (1) via telescopic transmission shafts (25, 25') and bevel gear drives (26, 26') fitted on the outsides of the wheels on both individual sets of running gear (2, 2'). Thus, when the vehicle is taking a curve, the angle formed between a leading body unit beneath which there is such a set of running gear and a trailing body unit also supported on an axle is transmitted to the steerable individual running gears units so that the pairs of wheels assume the desired radial position.