Stepclimb from RVSM to Metric in Vnav = Freeze

[hopskip 251]

So Today I was flying VIDP - ZMUB via DCT N451F370 DPN L626 HW 32N081E/K0829S1130 QIM NUKTI OWOOT/K0832S1210 B10 KATBA B480A UDA DCT At the step climb to Metric, I opened the "MTRS" in the PFD, selected 37100 on the MCP, Selected CRZ on the captains CDU and then typed in 37100 and selected this as the new cruise altitude and hit exec. The aircraft began to climb the 100ft to the new altitude. As it reached 37100 the PFD showed that the aircraft had captured the altitude, and suddenly it was frozen. The PFD showed FL371 with about 300ft per min climb rate. but the autopilot had started to pitch down to capture altitude. It continued to pitch down, and down, and more down. So I hit the autopilot disconnect. which did nothing. So I turned the yoke full right deflection. nothing happened. The aircraft was trucking straight ahead and going down. fast. Pulling the throttle did nothing. however pressing F1 and F4 did produce min/max thrust on command. Clicking Fuel Cutoff switches to "Cutoff" resulted in... the engines still running. ... Tried a second time and using V/S Mode from FL370 to FL371 worked. Changed the CDU after maintaining the new cruise in ALT HLD mode. An hour or so later it was time to leave China's RVSM Metric and enter Mongolia's Metric. VNAV climb selected for 12100m, aka 39700ft. Again as the aircraft captured altitude in VNAV - instant freeze. This time I rode it down through a few oscillations and managed to use the F1/F2/F3/F4 and E 1 and 2 keys to make a differential thrust turn, and control my decent. Landing gear handle would not budge from "off" and the flap lever could not move. Eventually belly-crashed the aircraft into the sands of the Gobi Desert. This is the first time I have experienced the "Freeze" and am wondering if it is related to capturing the altitude in VNAV when the altitude is an odd one like FL397 or FL371. Or if the FMC did not like that altitude put into it as the final cruise altitude. or something else entirely. I'v done Step Climbs before. usually to RVSM levels. and these have been done in VNAV using the "Select altitude on MCP - Select altitude in CRZ page on the CDU - Click Exe" method. None of these have resulted in a freeze before. Regards,Trent Hopkinson