The present invention is directed to an apparatus for assembling a uniform-speed joint having an inner rotary body and an outer rotary body which transmits a rotational force from one to the other through a plurality of small spheres disposed in receiving holes in the outer peripheral surface of the inner rotary body. The apparatus comprises a carrying member for carrying the outer rotary bodies such that the inner surface of the rotary body is oriented upward and guide members, including a first guide wall, a second guide wall and a pusher for pushing an inner rotary body along the first guide wall until it contacts the second guide wall. The apparatus also comprises a first press fitting member for press fitting two small spheres into diametrically opposed receiving holes in the inner body and clamping members for clamping the inner rotary body, orienting the axis of the inner rotary member perpendicular to the axis of said outer rotary member on the carrying member and inserting the inner rotary member into the outer rotary member. Correcting members are provided for orienting the inner rotary body with respect to the outer rotary body such that the axis of the inner rotary body coincides with the axis of the outer rotary body. The apparatus further comprises swing members for rotating the inner rotary body in the outer rotary body such that at least one of the receiving holes is above the top edge of the outer rotary body and second press fitting members for pressing the small spheres into the receiving holes above the top edge of the outer rotary body.