CE560 First Officer reported runaway pitch trim at FL400 resulting in a 1000 foot ascent before the the climb could be arrested. A descent to FL370 then ensues before the aircraft is returned to FL400. No further problems with the autopilot or trim are encountered and the flight continues to destination.

Narrative

While Cruising at FL400 during a clear day with no apparent turbulence and the auto pilot engaged; the auto pilot started an abrupt climb. The flying pilot took control of the yoke and initially tried using the TCS [Touch Control Steering] button to correct then climb. When the flying pilot was aware that the TCS was not enough to counter the effects of the climb he used the electric pitch trim to apply nose forward trim which disconnected the autopilot and started applying nose down trim. At this point seeing the aircraft was about to fly through the 300 ft RVSM deviation limit I advised ATC that we were in an uncontrollable climb. I also hit the auto pilot disconnect just to make sure that the procedure had been done. At about FL410 we were able to level off and get temporary control. The flying pilot started to descend but now felt that the yoke was too nose forward and we were unable to level at FL400 and continued down. At this point realizing we were in an uncontrollable descent I called a Mayday and told ATC that we were unable to control the plane and needed block altitude FL350-FL410. ACT approved the block and asked if we needed further assistance. I advised ATC to stand by. At FL370 we regained control and the flying pilot started to climb back to FL400. At this point we ran every trim check and reviewed every emergency checklist that pertained to our experience and it seemed that all checks and equipment were functioning normally. I canceled the Mayday with ATC and advised them that we were going to continue to destination airport as we were almost there anyway. My personal thoughts are that the trim auto trimmed aft and it took the pilot a thousand feet to recover. As far as the descent we did have full forward trim and I believe again that the pilot took an excessive amount of altitude to recover due to thin air and possibly the flying pilot being easy on the controls in order to keep from overloading the aircraft.