The rolling-bearing unit with reduction gear of this invention includes, an outer ring or race having outer ring raceways formed on its inside circumferential surface, an inner ring or race having inner ring raceways formed on its outside circumferential surface and which face the outer ring raceways, several rolling bodies located between the outer ring raceways and inner ring raceways, a ring gear formed on the inside circumferential surface of a member which is affixed with respect to the outer ring or race and which is located away from the outer ring raceway in the axial direction, several support shafts which are connected respectively at their base portion at circumferential locations on the end face of the inner ring or race and arranged so that they are parallel to the outer and inner rings or races, and planetary gears which are rotatably supported around the support shafts and which mesh with the ring gear.