On October 20, 1997, at 1645 eastern daylight time, a Mooney M20C, N3426X, veered off the left side of runway 32, according to the pilot, during a full stop landing at the Hendersonville Airport in Hendersonville, North Carolina. The personal flight operated under the provisions of Title 14 CFR Part 91 with no flight plan filed. Weather data recovered from the nearest reporting facility disclosed that visual weather conditions prevailed at the time of the accident. The private pilot reported that he was not injured, and the airplane sustained substantial airframe damage. According to the pilot, the local flight departed Hendersonville, North Carolina, at approximately 1600. The pilot said that, following the initial takeoff, he remained in closed traffic to complete three full stop landings. During the first landing, the pilot reported that he experienced some difficulty maintaining directional control of the airplane after each landing. On the second landing, the airplane became more difficult to control, veered off the left side of the runway, and begun to skid. During the skidding maneuver, the nose gear assembly was torn from the airframe, and the right main landing gear collapsed in the opposite direction of normal retraction. The airplane came to rest approximately 1500 feet from the approach end of the 3000 foot long runway. The pilot also reported that the runway surface had undergone several previous repairs, and the surface was rough and uneven. The airplane touched down within the rough and uneven portion of the runway surface. During a telephone conversation with the pilot, he stated that, prior to the accident the airplane had under gone extensive maintenance to the nose gear assembly. The maintenance included the completion of a Mooney Service Bulletin (SB). The purpose of SB M20-202 is to provide instructions for checking the location of the nose wheel for optimum tracking during high speed ground operations. The pilot stated that the nose wheel steering linkage was replaced and that the nose wheel steering shock assembly was also removed in accordance with the airframe maintenance instructions. Following the nose gear repairs, the pilot stated that the high speed nose wheel steering and controllability were more difficult than before the repairs were completed. The mechanic continued making adjustments to the nose gear in an effort to correct the steering problems. The nose gear repairs and adjustments failed to correct the high speed ground handling control problem. The pilot stated that, during the post accident examination of the nose steering assembly, it was discovered that the nose wheel steering linkage had failed. An inquiry, by the aircraft owner with the previous owner, disclosed that the previous owner has experienced several failures of the nose wheel steering linkage assembly. Subsequent to this accident the owner discovered several articles written by M-20 owners who have experienced high speed nose wheel control problems.