A wave generator for a strain wave gearing, the wave generator comprising a rigid wave plug and a wave bearing; an inner-race inner peripheral surface of the wave bearing being secured by press-fitting and an adhesive to a non-circularly contoured plug external peripheral surface of the wave plug; characterised in that the plug external peripheral surface and/or the inner-race inner peripheral surface having a groove formation surface in which adhesive-retaining grooves capable of retaining the adhesive are formed; wherein adhesive-retaining grooves are microgrooves being of no greater than micrometer-order width and depth; the groove formation surface is formed with an arrangement pattern having a plurality of the microgrooves; and the arrangement pattern is either one of: a first-direction arrangement pattern, in which microgrooves extend in straight lines or curved lines in a first direction at a fixed pitch; and an intersecting arrangement pattern, in which the first-direction arrangement pattern and a second direction arrangement pattern are formed in an intersecting state, the second-direction arrangement pattern having microgrooves extending in straight lines or curved lines in a second direction at a fixed pitch; wherein the groove formation surface includes a first groove formation surface formed on one of the plug external peripheral surface and the inner-race inner peripheral surface and a second groove formation surface formed on the other thereof; wherein each of the first and second groove formation surfaces (43A, 45A) is formed with the first-direction arrangement pattern or the intersecting arrangement pattern; wherein the plug external peripheral surface has an ellipsoidal shape; and wherein in the groove formation surface, a depth of the microgrooves formed in portions where a long axis of the ellipsoidal shape is positioned is shallower than a depth of the microgrooves formed in portions where a shot axis of the ellipsoidal shape is positioned. a rigid wave plug and a wave bearing; an inner-race inner peripheral surface of the wave bearing being secured by press-fitting and an adhesive to a non-circularly contoured plug external peripheral surface of the wave plug; characterised in that the plug external peripheral surface and/or the inner-race inner peripheral surface having a groove formation surface in which adhesive-retaining grooves capable of retaining the adhesive are formed; wherein adhesive-retaining grooves are microgrooves being of no greater than micrometer-order width and depth; the groove formation surface is formed with an arrangement pattern having a plurality of the microgrooves; and the arrangement pattern is either one of: a first-direction arrangement pattern, in which microgrooves extend in straight lines or curved lines in a first direction at a fixed pitch; and an intersecting arrangement pattern, in which the first-direction arrangement pattern and a second direction arrangement pattern are formed in an intersecting state, the second-direction arrangement pattern having microgrooves extending in straight lines or curved lines in a second direction at a fixed pitch; wherein the groove formation surface includes a first groove formation surface formed on one of the plug external peripheral surface and the inner-race inner peripheral surface and a second groove formation surface formed on the other thereof; wherein each of the first and second groove formation surfaces (43A, 45A) is formed with the first-direction arrangement pattern or the intersecting arrangement pattern; wherein the plug external peripheral surface has an ellipsoidal shape; and wherein in the groove formation surface, a depth of the microgrooves formed in portions where a long axis of the ellipsoidal shape is positioned is shallower than a depth of the microgrooves formed in portions where a shot axis of the ellipsoidal shape is positioned. a first-direction arrangement pattern, in which microgrooves extend in straight lines or curved lines in a first direction at a fixed pitch; and an intersecting arrangement pattern, in which the first-direction arrangement pattern and a second direction arrangement pattern are formed in an intersecting state, the second-direction arrangement pattern having microgrooves extending in straight lines or curved lines in a second direction at a fixed pitch; wherein the groove formation surface includes a first groove formation surface formed on one of the plug external peripheral surface and the inner-race inner peripheral surface and a second groove formation surface formed on the other thereof; wherein each of the first and second groove formation surfaces (43A, 45A) is formed with the first-direction arrangement pattern or the intersecting arrangement pattern; wherein the plug external peripheral surface has an ellipsoidal shape; and wherein in the groove formation surface, a depth of the microgrooves formed in portions where a long axis of the ellipsoidal shape is positioned is shallower than a depth of the microgrooves formed in portions where a shot axis of the ellipsoidal shape is positioned.