G100/Astra 1125 Captain reported a loss of control while using an auto-flight constant mach setting during climb. Pilot surmised an encounter with severe mountain wave and diverted to an alternate airport to check for damage.

Narrative

After departing ZZZ during the climb phase the aircraft was configured in the Mach hold setting of '.68' with an AOA indicating '.3' while maintaining around 4-8 hundred FPM climb to FL370. At about 1-2 hundred FT prior to reaching FL370 the vertical speed showed a rapid descent to 2000FPM while the altimeter showed a descending trend as well. My first thought was the airplane had stalled so I performed the appropriate stall recovery to lower the Angle of attack to break the stall and add max power. this caused the FL change from near FL370 down to around FL340 at this time ATC had asked what was going on and that they had shown us in a decent and loss of around 5 thousand feet. At this time we had asked for a block altitude and began a climb to correct; when we began to lose altitude again in the second climb we requested a lower altitude of FL300 until we could maintain positive control of the aircraft. Once I had control of the aircraft and began to trouble shoot what may have caused this descent I advised ATC and diverted to ZZZ1 to confirm there was no damage or malfunction to any flight control or cowlings. After consulting with mentor pilots who have flown in this area before and confirming exact location of the event I determined that I had experienced severe mountain wave which was something I had not personally experienced before. With this experience now I can take the corrective action if this happens again by maintaining a safe forward speed; requesting a block altitude and turning off the altitude hold on the autopilot to ensure the aircraft does not try to pitch to maintain altitude if the mountain wave forces the aircraft to change altitude