MD-80 holding at FL320 experienced a conflict with opposite direction traffic; resulting in two opposite direction RAs as well as a new clearance from ATC.

Narrative

Due to weather/congestion at our destination; we were given holding instructions by Memphis Center to hold Southwest of BWG on J6 at our current altitude of FL320. Using 2-engine Holding Performance for a 140K-lb aircraft at FL320; we calculated a conservative holding speed of 255 KTS. We entered holding. We requested and were given approval for 20-mile legs. Weather was partly cloudy at altitude. While established in holding we got a TA Alert 'Traffic; Traffic.' This aircraft had a TCAS display range of only 12NM. We could see the target at approximately 10 to 11 O'Clock relative to our position on the TCAS display. The target was at our altitude. The First Officer stated 'Be ready to maneuver.' Within seconds; the TCAS gave an RA Alert 'Descend; descend; descend.' The green arc commanded a descent rate of 1500 FPM. The Captain immediately disconnected the autopilot and autothrottles. Almost immediately afterwards; ATC directed us to turn left to a heading of 330 degrees. The First Officer stated that we were unable; because we were descending to comply with an RA. The target appeared to also be descending because the data remained at +00 to +/-01 (within 100 feet of our altitude). Again within seconds; the TCAS Alert changed to 'Climb; Climb Now; Climb; Climb Now; Climb; Climb Now'; requiring a 1500 FPM climb to get into the green arc. By this time; we had lost approximately 700-800 FT. The First Officer saw that our aircraft symbol and the target symbol overlapped. During the climb maneuver; the aircraft experienced a low-speed buffet and the airspeed was observed to be approximately 220 KTS. The stall recovery procedure was followed. No stall or stall warnings were encountered. A few seconds later; we received the TCAS Alert 'Clear of Conflict.' We immediately returned to the assigned holding pattern as we accelerated to approximately 260 KTS and leveled off at FL320. We notified ATC of the conflict and maneuvers we had performed. When we queried Memphis Center (ATC) as to what had just happened; we got a period of silence and then instructed to call after we landed. They gave no further information after another query; but did advise us that 'they were sorting it all out.' Upon landing; we had maintenance inspect the aircraft.