it is an object of the invention to provide a structure of an internal thread portion for preventing looseness which structure allows a reduction in the torque required for the threaded engagement with an external - thread member and prevents a seizure . an exit end portion of a self - locking nut is taperingly contracted over the entire circumference thereof so as to form a contracted internal thread portion having a conical section . in addition , ridges of the contracted internal thread portion are provided with corrugation continuing circumferentially . the diameter of an inscribed circle which links the extremities of projections in the corrugation is smaller than the minor diameter of the external - thread member which is to be engaged threadedly with the internal thread portion . with the external - thread member threadedly engaged with the internal thread portion , a plurality of projections press the root or flanks of the external - thread member and are thereby elastically compressed by the reaction , so as to clamp the external - thread member from outside . in accordance with this arrangement , the tightening torque can be reduced and a seizure is prevented .