ACR MLG GOT A COMPRESSOR STALL RECOVERING FROM A LOW SPEED BUFFET AS FLT CREW CLIMBED TO MAXIMUM ALT TO AVOID ENROUTE WX.

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CRUISING AT FL310 E OF ABQ ON J72. ENCOUNTERED NUMEROUS BUILDUPS AND TSTMS ON THE ARWY AND REQUESTED DEVIATION N OF COURSE. ATC APPROVED DEVIATION AND REQUESTED DSCNT TO FL290. AFTER SOME MANEUVERING WE REQUESTED FL350; WHICH WAS THE MAX ALT FOR OUT WT OF 128000#. WX WAS WORSENING AND WE HOPED TO CLB ABOVE IT. ATC CLRED US FROM FL290 TO FL350 AND REQUESTED WE EXPEDITE THROUGH FL330. CAPT WAS HANDLING THE RADIOS AND THE RADAR WHILE F/O WAS FLYING. AS THE ACFT PASSED THROUGH FL330 THE CAPT NOTICED THAT THE AIRSPD HAD FALLEN OFF TO .695 MACH. CAPT ADVISED F/O TO LEVEL OFF AND LET AIRSPD BUILD. NUMEROUS CALLS TO ATC PLUS RADAR INTERPRETATION DISTRACTED CAPT. THROUGH FL340 AT .678 MACH (PMS SHOWED .690 MACH FOR MAX CLB). CAPT AGAIN ADVISED F/O TO LEVEL OFF AND BUILD AIRSPD. AT .700 MACH F/O STARTED 200 FPM CLB TO FL350. ATC WAS GETTING CONCERNED ABOUT TFC AND GAVE US A 20 DEG TURN TO THE LEFT AND TO CALL LEVEL AT FL350. AS ACFT LEVELED AT FL350; WE ENCOUNTERED TURB AND MACH FELL OFF TO .670 FOLLOWED IMMEDIATELY BY LOW SPD BUFFET. CAPT PUSHED THROTTLES TO FIREWALL AND STARTED DSCNT TO FL340. ATC ADVISED OF DSCNT. APPARENTLY #1 ENG EXPERIENCED A COMPRESSOR STALL AS PWR FELL OFF MOMENTARILY AND CAME BACK UP TO FULL PWR. I SURMISE IT WAS A COMPRESSOR STALL BECAUSE THE F/A'S (LATER IN THE DAY) RPTED A POPPING SOUND CAME FROM THE LEFT ENG. AIRSPD BUILT TO MACH .760 AT FL340 AND A NORMAL CLB TO FL350 TOOK PLACE. FLT CONTINUED TO LAS WITH NO OTHER UNUSUAL EVENTS. I THINK 2 FACTORS CONTRIBUTED TO THE PROB. THE WORKLOAD OF A 2-M ACFT IN WX OPERATING IN HIGH DENSITY AIR TFC ENVIRONMENT DID NOT ALLOW SUFFICIENT TIME TO CHK PROGRESS OF PF. THE SECOND CONTRIBUTOR WAS THE PF BEING PREOCCUPIED WITH VERT SPD; TO PLEASE ATC; RATHER THAN MAINTAINING A SAFE AIRSPD AND ACCEPTING THE RATE OF CLB AVAILABLE. PREVENTION; IN THE FUTURE; LIES IN RE-EDUCATING PLTS ON THE NECESSITY OF ADEQUATE AIRSPD WHEN OPERATING NEAR MAX HABITABLE ALT. SUPPLEMENTAL INFO FROM ACN 91667: WE HAD NO INDICATION THAT WE WERE OPERATING OUTSIDE THE PERFORMANCE CAPABILITY OF THE ACFT AS WE TOOK THOSE STEPS. THE PMS STATED THAT WE COULD DO WHAT WE DID. WE AT NO TIME RECEIVED AN INDICATION VIA THE FMA THAT OUR SPD WAS TOO LOW. ON THE GND WE CONSULTED THE OPERATING MANUAL AND IT CONCURRED WITH THE DATA PRESENTED BY PMS AS WELL AS STATED THAT WE WERE NOT IN THE LOW SPD BUFFET RANGE. I BELIEVE THE COMPRESSOR STALL RESULTED FROM TOO FAST A THROTTLE MOVEMENT ON THE PART OF THE CAPT. TURB MAY HAVE BEEN A FACTOR BUT I DON'T THINK IT WAS THE PRIMARY CAUSE.