A DC9 CREW EXPERIENCED ACFT DECELERATION AT LEVELOFF; L TRAILING EDGE FLAP EXTENDED 3 INCHES.

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AT LEVELOFF AT FL350; ACFT WOULD NOT ACCELERATE AND STARTED TO DECELERATE. PLT IN REAR OF ACFT INDICATED THAT L FLAP WAS EXTENDED 3 INCHES. ACFT CONTINUED TO DECELERATE. REQUESTED IMMEDIATE DSCNT TO FL310 WHICH THEY COULD NOT APPROVE IMMEDIATELY. DUE TO ACFT PERFORMANCE WE HAD TO INITIATE A SHALLOW DSCNT; APPROX 400 FT BELOW FL350 UNTIL CLRNC WAS RECEIVED FOR LOWER. DID NOT FEEL IT PRUDENT TO MAINTAIN FL350 WITH AIRSPD DECREASING. SUPPLEMENTAL INFO FROM ACN 505127: PLT IN AFT CABIN RPTED L FLAP EXTENDED 3 INCHES WHEN R RETRACTED. COULD NOT MAINTAIN FL350 WITHOUT AIRSPD DECREASING. CALLBACK CONVERSATION WITH RPTR ACN 505126 REVEALED THE FOLLOWING INFO: RPTR STATED THE ACFT; ALTHOUGH REQUIRING EXTRA PWR AND TRIM; DID PERFORM ADEQUATELY AT FL310. WHILE TROUBLESHOOTING; THE HYD SYS WAS REPRESSURIZED IN HOPES THE FLAPS WOULD FAIR TO THEIR NORMAL POS. HOWEVER; THEY REMAINED IN THE EXTENDED POS (3 INCHES) UNTIL APPROX 16000 FT ON DSCNT; AT WHICH TIME THEY RETRACTED (FAIRED) TO THE UP POS. FLAP OP WAS RPTED AS NORMAL DURING DSCNT AND APCH. RPTR HAS HAD NO FEEDBACK FROM MAINT AS TO THEIR FINDINGS.