On March 4, 2002, about 1230 central standard time, a Beech Baron, BE-55, N66X, sustained minor damage during a mid-air collision with a Piper Archer, PA-28-181, N9272L, 20 miles southeast of Springfield, Missouri. The Archer also received minor damage. The certified flight instructor (CFI), the commercial dual student pilot, and two passengers who were on board the Baron reported no injuries. The commercial pilot flying the Archer was not injured. The 14 CFR Part 91 instructional flight originated from Mountain Home (BPK), Arkansas, en route to Lee's Summit (LXT), Missouri. The Archer that was on a 14 CFR Part 91 repositioning flight, had also departed BPK en route to LXT. The Archer departed at 1145 and the Baron departed about 1200. The airplanes were not flying a formation flight. Both airplanes were flying at 6,500 feet msl direct to LXT on an approximate heading of 330 degrees. The Baron overtook the Archer. When the CFI in the Baron saw the Archer, he pushed the yoke forward and attempted to fly under the Archer. The vertical stabilizer of the Baron struck the left main landing gear of the Archer. After the incident, the Baron made a precautionary landing at Springfield (SGF), Missouri, and the Archer continued en route and landed uneventfully at LXT. Visual meteorological conditions prevailed and neither airplane was on a flight plan. The Baron pilot reported that he had flown the pilot of the Archer, along with a student pilot and two other passengers, from LXT to BPK earlier in the day. The purpose of the flight was to drop off the pilot of the Archer so he could ferry the Archer back to LXT. The Baron pilot reported that once they were on the ground at BPK, the pilot of the Archer prepared to get the Archer ready for takeoff. The Baron pilot reported that he did not talk with the Archer pilot about what altitudes or routes that either pilot planned to use on the return trip to LXT. The Baron pilot reported that he was briefing his commercial rated student pilot when the Archer departed about 1145. The Baron pilot reported the Baron departed about 1200 and climbed to 6,500 feet msl direct to LXT. He reported that he was in the right seat giving flight instruction regarding various instrument flight rules, multi-engine procedures, and emergency procedures during the flight back to LXT. He reported that he started discussing emergency procedures involving the manual landing gear extension procedures. He reported, "While saying this, I pointed down to the floorboard at the indicator for 2-3 seconds when I heard an expletive from the backseat and looked up. I saw two wheels and a fuselage and immediately pushed forward on the controls and felt a bump. Someone in the back seat immediately said we hit them, I then realized we had just hit an aircraft. I made a shallow turn to the right to make visual contact and the passengers told me it appeared to be the Archer, and that it appeared to be OK. I then immediately made a turn towards Springfield Regional." The pilot reported he made an uneventful landing at SGF. The Archer pilot reported he departed BPK and climbed to 6,500 feet msl, turned on the autopilot, and set the heading bug for a direct flight back to LXT. He reported that about 15 to 20 miles from SGF something slammed into the airplane that lifted the left wing. He reported, "At the same time a twin came up from under me and climbed slightly and turned to the right. Then I caught the turbulence from his plane, my motor shuddered...the autopilot corrected my plane back to straight and level flight. I checked all my gages everything seamed ok." He reported he did not know if there was any damage to the airplane but it flew fine. He continued on course and landed safely at LXT.