ASRS 1609145

While cruising at FL360, we were told by ATC Center to descend in less than 2 minutes to FL340, and turn to heading 220. I am not sure what order those instructions were given. I was the Pilot Flying. I decided to initially start my descent around 2,000 feet a minute, to guarantee compliance. I uncoupled altitude hold on the APS-80 autopilot, and engaged altitude select, I started the airplane descending by rolling the autopilot vertical trim wheel down. The only way to know how much trim has been imputed is by watching the airplane react. I also selected the heading mode and turned the airplane to [heading] 220, I am not sure about the sequence. The airplane was descending at 2,000 feet per minute plus, at approximately 35,000 feet, I used the autopilot trim wheel to slow the descent. After slowing the descent and at approximately 34,400 feet, both pilots called out that the altitude select mode was engaged, because we know that it is imperative to check that the altitude select mode is engaged, as it sometimes disengages without warning. We both saw the airplane leveling at FL340. ATC Center gave us a direct to ZZZZZ intersection and a frequency change. I [entered] Direct to ZZZZZ in the left FMS, while the other pilot changed frequencies and updated his FMS.I looked at the altimeter and noticed that the airplane was climbing through approximately 35,000 feet at a high rate of climb. I did not hear an altitude alert. I shouted a couple of expletives getting the other pilots attention, disengaged the autopilot and rapidly descended back to FL340. During that time, I heard our TCAS I report a traffic alert. I looked out the window, but did not see any traffic. We were also given instructions by ATC Center again to descend to FL340 during the time we were recovering from the uncommanded climb. The most reasonable answer for this situation is a late and over- correcting with the autopilot trim wheel, but to the best of my knowledge I did not do that. I also fly a Falcon 10 with a similar autopilot. The little experience I have had with these airplanes has taught me not to over correct or correct the rate of assent or descent close to the programmed altitude. It is possible that we had a trim malfunction or runaway. I have experienced autopilot runaway on older airplanes with similar autopilots. Although we were not excessively busy, the need for an immediate descent, a heading change, a Direct to, and a frequency change in less than two minutes was probably a contributing factor, taking our full attention from noting a total completion of the level off.