A friction roller-type reduction gear comprising: a sun roller arranged concentrically with an input shaft; a ring roller arranged concentrically with the sun roller at an outer periphery-side of the sun roller; a plurality of intermediate rollers supported to be rotatable about a rotation shaft parallel with the input shaft between an outer peripheral surface of the sun roller and an inner peripheral surface of the ring roller and configured to be in rolling contact with the outer peripheral surface of the sun roller and the inner peripheral surface of the ring roller, and a loading cam mechanism configured to change a contact surface pressure of a rolling contact surface of each roller, wherein the ring roller includes a pair of roller elements (27, 29) provided in parallel in an axial direction of the input shaft, wherein at least one of the pair of roller elements (27, 29) is a moveable roller element configured to be moveable axially, wherein the loading cam mechanism is arranged at only an outer end face-side of the moveable roller element in the axial direction and is configured to displace the moveable roller element towards the other roller element in correspondence to rotation torque of the input shaft, wherein the outer peripheral surface of the sun roller is a concave curved surface of which a shape of an outer edge in an axial cross-section is a single circular arc-shaped concave curve, and wherein an outer peripheral surface of the intermediate roller is a convex curved surface of which a shape of an outer edge in an axial cross-section is a single circular arc-shaped convex curve, characterized in that the friction roller-type reduction gear comprises a coupling part configured to couple the ring roller and an output shaft, and that one of the following two inequalities is satisfied, wherein n ⋅ μ tan α < 1 is satisfied, when the inner peripheral surface of the ring roller is configured as a tapered traction surface for converting an axial load into a normal force and the outer peripheral surface of the sun roller is configured as a traction surface having no contact angle with the intermediate roller or when the outer peripheral surface of the sun roller is configured as a tapered traction surface for converting an axial load into a normal force and the inner peripheral surface of the ring roller is configured as a traction surface having no contact angle with the intermediate roller, wherein n ⋅ μ 2 ⋅ tan α < 1 is satisfied, when the outer peripheral surface of the sun roller and the inner peripheral surface of the ring roller both are configured as tapered traction surfaces for converting an axial load into a normal force, wherein μ = traction coefficient, α = inclination angle of a tapered traction surface and n = number of the intermediate rollers of the friction roller-type reduction gear. a sun roller arranged concentrically with an input shaft; a ring roller arranged concentrically with the sun roller at an outer periphery-side of the sun roller; a plurality of intermediate rollers supported to be rotatable about a rotation shaft parallel with the input shaft between an outer peripheral surface of the sun roller and an inner peripheral surface of the ring roller and configured to be in rolling contact with the outer peripheral surface of the sun roller and the inner peripheral surface of the ring roller, and a loading cam mechanism configured to change a contact surface pressure of a rolling contact surface of each roller, wherein the ring roller includes a pair of roller elements (27, 29) provided in parallel in an axial direction of the input shaft, wherein at least one of the pair of roller elements (27, 29) is a moveable roller element configured to be moveable axially, wherein the loading cam mechanism is arranged at only an outer end face-side of the moveable roller element in the axial direction and is configured to displace the moveable roller element towards the other roller element in correspondence to rotation torque of the input shaft, wherein the outer peripheral surface of the sun roller is a concave curved surface of which a shape of an outer edge in an axial cross-section is a single circular arc-shaped concave curve, and wherein an outer peripheral surface of the intermediate roller is a convex curved surface of which a shape of an outer edge in an axial cross-section is a single circular arc-shaped convex curve, characterized in that the friction roller-type reduction gear comprises a coupling part configured to couple the ring roller and an output shaft, and that one of the following two inequalities is satisfied, wherein n ⋅ μ tan α < 1 is satisfied, when the inner peripheral surface of the ring roller is configured as a tapered traction surface for converting an axial load into a normal force and the outer peripheral surface of the sun roller is configured as a traction surface having no contact angle with the intermediate roller or when the outer peripheral surface of the sun roller is configured as a tapered traction surface for converting an axial load into a normal force and the inner peripheral surface of the ring roller is configured as a traction surface having no contact angle with the intermediate roller, wherein n ⋅ μ 2 ⋅ tan α < 1 is satisfied, when the outer peripheral surface of the sun roller and the inner peripheral surface of the ring roller both are configured as tapered traction surfaces for converting an axial load into a normal force, wherein μ = traction coefficient, α = inclination angle of a tapered traction surface and n = number of the intermediate rollers of the friction roller-type reduction gear.