A rear wheel steering apparatus for a vehicle, comprising: a housing configured to be connected to a suspension mechanism supporting vehicle rear wheels via a first connection member and a second connection member, the housing including a cylinder portion and a connection cover; an electric motor housed in the housing; a speed reduction mechanism housed in the housing and reducing speed of an output of the electric motor; a linear motion mechanism including a nut member rotatably connected to the speed reduction mechanism, the linear motion mechanism including a rod threadingly engaged with the nut member and connected to the second connection member, the linear motion mechanism converting a rotation of the nut member to a linear motion of the rod; the cylinder portion housing the electric motor and the speed reduction mechanism which are arranged in series, the cylinder portion including a stopper portion (10a, 14) provided at an inner surface of the cylinder portion between the electric motor and the speed reduction mechanism; the connection cover including the first connection member and closing an opening of the cylinder portion provided closer to the speed reduction mechanism; a cylindrical holding member holding the speed reduction mechanism in the cylinder portion; and a bearing supporting the nut member for allowing the nut member to rotate relative to the cylindrical holding member; wherein the bearing and the cylindrical holding member are sandwiched between the stopper portion (10a, 14) of the cylinder portion and the connection cover and the cylindrical holding member is retained so as not to rotate relative to the cylinder portion, wherein the stopper portion corresponds to a snap ring fixed to an annular groove provided at an inner periphery surface of the cylinder portion and wherein the cylinder portion and the connection cover are fastened by an annular lock nut, wherein the speed reduction mechanism is structured with a planetary gear mechanism which includes a sun gear with an external gear, planetary gears with external gears and a ring gear with an internal gear, wherein grooves (34c, 34c) opening in an axial direction and opening through inner peripheral surfaces of the cylindrical holding member are formed on a peripheral wall of the cylindrical holding member, wherein the ring gear integrally includes a pair of engaging portions (33e, 33e) that extend radially outward and wherein a protrusion is formed at each of side surfaces of the engaging portions (33e, 33e) and when inserting the ring gear in the cylindrical holding member, the ring gear is fitted to the cylindrical holding member while the protrusions (33f, 33f) of the engaging portions (33e, 33e), respectively, are pressed onto inner side surfaces of the grooves (34c, 34c). a housing configured to be connected to a suspension mechanism supporting vehicle rear wheels via a first connection member and a second connection member, the housing including a cylinder portion and a connection cover; an electric motor housed in the housing; a speed reduction mechanism housed in the housing and reducing speed of an output of the electric motor; a linear motion mechanism including a nut member rotatably connected to the speed reduction mechanism, the linear motion mechanism including a rod threadingly engaged with the nut member and connected to the second connection member, the linear motion mechanism converting a rotation of the nut member to a linear motion of the rod; the cylinder portion housing the electric motor and the speed reduction mechanism which are arranged in series, the cylinder portion including a stopper portion (10a, 14) provided at an inner surface of the cylinder portion between the electric motor and the speed reduction mechanism; the connection cover including the first connection member and closing an opening of the cylinder portion provided closer to the speed reduction mechanism; a cylindrical holding member holding the speed reduction mechanism in the cylinder portion; and a bearing supporting the nut member for allowing the nut member to rotate relative to the cylindrical holding member; wherein the bearing and the cylindrical holding member are sandwiched between the stopper portion (10a, 14) of the cylinder portion and the connection cover and the cylindrical holding member is retained so as not to rotate relative to the cylinder portion, wherein the stopper portion corresponds to a snap ring fixed to an annular groove provided at an inner periphery surface of the cylinder portion and wherein the cylinder portion and the connection cover are fastened by an annular lock nut, wherein the speed reduction mechanism is structured with a planetary gear mechanism which includes a sun gear with an external gear, planetary gears with external gears and a ring gear with an internal gear, wherein grooves (34c, 34c) opening in an axial direction and opening through inner peripheral surfaces of the cylindrical holding member are formed on a peripheral wall of the cylindrical holding member, wherein the ring gear integrally includes a pair of engaging portions (33e, 33e) that extend radially outward and wherein a protrusion is formed at each of side surfaces of the engaging portions (33e, 33e) and when inserting the ring gear in the cylindrical holding member, the ring gear is fitted to the cylindrical holding member while the protrusions (33f, 33f) of the engaging portions (33e, 33e), respectively, are pressed onto inner side surfaces of the grooves (34c, 34c).