A kneading screw comprising: a screw body comprising a feed section and a kneading section, said feed section comprising a screw segment for feeding a to-be-kneaded material to a downstream side, said kneading section comprising a kneading segment for kneading the material, said screw body further comprising a multi-stage portion (18a, 18b) having rotating outside diameters changing gradually axially, said multi-stage portion (18a, 18b) being formed in at least one of a connection between said kneading section and another section adjacent to said kneading section, and the interior of said kneading section, wherein said multi-stage portion (18a, 18b) is formed so as to compensate between two segments different in rotating outside diameter, characterized in that when a stepped portion is formed between any of segments (21 to 24) constituting said multi-stage portion (18a, 18b) and a segment adjacent thereto, and assuming the outside diameter of a spline shaft as a steel shaft extending axially through said multi-stage portion (18a, 18b) to be D, each difference [δ] in height in the radial direction of said multi-stage portion (18a, 18b) satisfies the relation of the following expression: δ / D 3 ≤ 4, 0 E − 06 1 / mm 2 δ: difference in height of each stepped portion constituting said multi-stage portion (18a, 18b), (mm) D: outside diameter of said spline shaft, (mm), wherein when n number of said differences in height are present between two segments adjacent to said multi-stage portion (18a, 18b), and assuming the outside diameter of said spline shaft extending axially through said multi-stage portion (18a, 18b) to be D, the difference Δ in rotating outside diameter between said two segments satisfies the relation of the following expression: Δ / D 3 ≤ 4.0 E − 06 × n 1 / mm 2 Δ: difference in rotating outside diameter between two segments, (mm) D: outside diameter of said spline shaft, (mm) n: number of difference in height formed between said two segments. a screw body comprising a feed section and a kneading section, said feed section comprising a screw segment for feeding a to-be-kneaded material to a downstream side, said kneading section comprising a kneading segment for kneading the material, said screw body further comprising a multi-stage portion (18a, 18b) having rotating outside diameters changing gradually axially, said multi-stage portion (18a, 18b) being formed in at least one of a connection between said kneading section and another section adjacent to said kneading section, and the interior of said kneading section, wherein said multi-stage portion (18a, 18b) is formed so as to compensate between two segments different in rotating outside diameter, characterized in that when a stepped portion is formed between any of segments (21 to 24) constituting said multi-stage portion (18a, 18b) and a segment adjacent thereto, and assuming the outside diameter of a spline shaft as a steel shaft extending axially through said multi-stage portion (18a, 18b) to be D, each difference [δ] in height in the radial direction of said multi-stage portion (18a, 18b) satisfies the relation of the following expression: δ / D 3 ≤ 4, 0 E − 06 1 / mm 2 δ: difference in height of each stepped portion constituting said multi-stage portion (18a, 18b), (mm) D: outside diameter of said spline shaft, (mm), wherein when n number of said differences in height are present between two segments adjacent to said multi-stage portion (18a, 18b), and assuming the outside diameter of said spline shaft extending axially through said multi-stage portion (18a, 18b) to be D, the difference Δ in rotating outside diameter between said two segments satisfies the relation of the following expression: Δ / D 3 ≤ 4.0 E − 06 × n 1 / mm 2 Δ: difference in rotating outside diameter between two segments, (mm) D: outside diameter of said spline shaft, (mm) n: number of difference in height formed between said two segments. δ: difference in height of each stepped portion constituting said multi-stage portion (18a, 18b), (mm) D: outside diameter of said spline shaft, (mm), wherein when n number of said differences in height are present between two segments adjacent to said multi-stage portion (18a, 18b), and assuming the outside diameter of said spline shaft extending axially through said multi-stage portion (18a, 18b) to be D, the difference Δ in rotating outside diameter between said two segments satisfies the relation of the following expression: Δ / D 3 ≤ 4.0 E − 06 × n 1 / mm 2 Δ: difference in rotating outside diameter between two segments, (mm) D: outside diameter of said spline shaft, (mm) n: number of difference in height formed between said two segments. Δ: difference in rotating outside diameter between two segments, (mm) D: outside diameter of said spline shaft, (mm) n: number of difference in height formed between said two segments.