Abstract: A method of mounting a torque converter on a transmission comprises the steps of setting the transmission to have the tubular members extending horizontally, holding the torque converter by holding means which is movable in vertical and horizontal directions, positioning the torque converter to cause an imaginary axis of a turbine runner in the torque converter to coincide with a common imaginary axis of two coaxial tubular members in the transmission, moving the torque converter toward the transmission in the horizontal direction so as to engage an engaging portion of the turbine runner with an end portion of an inner one of two coaxial tubular members of the transmission, positioning further the torque converter to cause an imaginary axis of a stator in the torque converter to coincide with the common imaginary axis of two tubular members; and moving further the torque converter toward the transmission in the horizontal direction so as to engage an engaging portion of the stator with an end portion of an ou