On November 10, 2001, an Extra-Flugzeugbau GMBH EA300/L, N2XA, registered to Aero Sport Inc., operating as a 14 CFR Part 91 demonstration flight, and a James D. Smith RV-3, N93HS, registered to a private owner, operating as a 14 CFR Part 91 personal flight, experienced a mid-air collision during landing flare touchdown at the St. Augustine Airport (SGJ), St. Augustine, Florida. Visual meteorological conditions prevailed and no flight plan was filed for either airplane. N2XA sustained minor damage and N93HS sustained substantial damage. The airline transport-rated pilot and private pilot-rated passenger on N2XA reported no injuries. The commercial pilot on N93HS reported no injuries. N2XA departed from SGJ about 30 minutes before the accident. N93HS departed from Haller Airpark (7FL4), Green Cove Springs, Florida, about 30 minutes before the accident. The pilot of N2XA stated he departed SGJ about 30 minutes before the accident to conduct a demonstration flight to a prospective buyer. They flew to a training area located about 20 miles southwest of SGJ and he demonstrated the airplane. Upon completion of the maneuvers, they returned to SGJ. They attempted radio contact with SGJ UNICOM was which uneventful, however they overheard other airplanes indicating that they were landing to runway 02. They continued toward the airport making radio calls in the blind concerning their position and made a 45-degree entry for a 800 feet left downwind to runway 02 behind a Cessna airplane. The Cessna landed and reported clearing the active runway while they were turning from base to final approach. The left wing of his airplane was down for a required left crosswind landing. He started to flare the airplane just past the numbers and felt a "bump" similar to a hard landing and observed what he thought was a wheel pan go past the canopy of his airplane. At first he thought he would make a go-around but elected to land straight ahead. Upon completion of the landing, he turned his airplane 90-degrees on the runway and observed an RV-3 on the runway. He continued turning his airplane and back taxied down the runway to the RV-3, stopped, and shut his airplane down. At no time during his entry into the traffic pattern or during his approach did he or his passenger hear any radio communication from the RV-3 pilot. The pilot of N93HS stated he departed 7FL4 about 30 minutes before the accident. He approached SGJ from the northwest and attempted to contact SGJ UNICOM which was uneventful. He overheard other airplane pilot's on the UNICOM radio (A Cessna and a Piper pilot indicated they were landing to runway 02 and a Falcon jet pilot indicated he was landing to runway 31.) He decided to over-fly the airport at 1,500 feet to verify the wind condition and speed. He over flew the airport and entered a left downwind at 900 feet. While on final approach for runway 02, he observed the Falcon jet back-taxing down runway 02. He initiated a go-around, reentered left traffic at 900 feet behind a Cessna. The Cessna landed and cleared the active runway. He reported his position on UNICOM on short final. As the wheels of his airplane were touching down on the runway, he immediately felt an impact coming from above. He looked and observed the Extra on the runway. He stopped his airplane and exited unassisted. At no time while he was in the traffic pattern did he see or hear the Extra pilot on the UNICOM frequency. Examination of N93HS by the FAA revealed that both wheels of N2XA struck the top of N93HS left wing and left elevator. In addition, N2XA right wing struck the top of N93HS vertical stabilizer and canopy. (For additional information see FAA Aviation Safety Inspector Statement an attachment to this report.) Review of 14 CFR Part 91.113 Right-of way rules states in paragraph (g) Landing...."When two or more aircraft are approaching an airport for the purpose of landing, the aircraft at the lower altitude has the right-of-way."