A driving force transmission apparatus, comprising: an outer rotating member that has a plurality of first spline teeth on its inner peripheral surface, the first spline teeth extending in a direction of a rotation axis; an inner rotating member that is provided radially inward of the outer rotating member, that is supported coaxially with the outer rotating member so as to be rotatable relative to the outer rotating member, and that has a plurality of second spline teeth on its outer peripheral surface, the second spline teeth extending in the direction of the rotation axis; a plurality of outer friction plates each having a plurality of first protrusions at its outer peripheral portion, the first protrusions engaging with the first spline teeth; a plurality of inner friction plates which are arranged alternately with the outer friction plates, and each of which has a plurality of second protrusions at its inner peripheral portion, the second protrusions engaging with the second spline teeth; and a pressing member that is arranged on one axial side of the outer friction plates and the inner friction plates, that has a plurality of third protrusions at its inner peripheral portion, the third protrusions engaging with the second spline teeth, and that axially moves along the second spline teeth to press the outer friction plates and the inner friction plates to thereby frictionally engage the outer friction plates with the inner friction plates, said driving force transmission apparatus being characterized in that where a gap angle, defining a backlash, in a circumferential direction between each of the first spline teeth of the outer rotating member and a corresponding one of the first protrusions of the outer friction plates is θ 1, a gap angle, defining a backlash, in the circumferential direction between each of the second spline teeth of the inner rotating member and a corresponding one of the second protrusions of the inner friction plates is θ 2 and a gap angle, defining a backlash, in the circumferential direction between each of the second spline teeth of the inner rotating member and a corresponding one of the third protrusions of the pressing member is θ 3, the inequality, θ 1 + θ 2 - θ 3 ≥ 1.0°, is satisfied. an outer rotating member that has a plurality of first spline teeth on its inner peripheral surface, the first spline teeth extending in a direction of a rotation axis; an inner rotating member that is provided radially inward of the outer rotating member, that is supported coaxially with the outer rotating member so as to be rotatable relative to the outer rotating member, and that has a plurality of second spline teeth on its outer peripheral surface, the second spline teeth extending in the direction of the rotation axis; a plurality of outer friction plates each having a plurality of first protrusions at its outer peripheral portion, the first protrusions engaging with the first spline teeth; a plurality of inner friction plates which are arranged alternately with the outer friction plates, and each of which has a plurality of second protrusions at its inner peripheral portion, the second protrusions engaging with the second spline teeth; and a pressing member that is arranged on one axial side of the outer friction plates and the inner friction plates, that has a plurality of third protrusions at its inner peripheral portion, the third protrusions engaging with the second spline teeth, and that axially moves along the second spline teeth to press the outer friction plates and the inner friction plates to thereby frictionally engage the outer friction plates with the inner friction plates, said driving force transmission apparatus being characterized in that where a gap angle, defining a backlash, in a circumferential direction between each of the first spline teeth of the outer rotating member and a corresponding one of the first protrusions of the outer friction plates is θ 1, a gap angle, defining a backlash, in the circumferential direction between each of the second spline teeth of the inner rotating member and a corresponding one of the second protrusions of the inner friction plates is θ 2 and a gap angle, defining a backlash, in the circumferential direction between each of the second spline teeth of the inner rotating member and a corresponding one of the third protrusions of the pressing member is θ 3, the inequality, θ 1 + θ 2 - θ 3 ≥ 1.0°, is satisfied.