B757 LEADING EDGE AND TRAILING EDGE FLAP DISAGREE MESSAGES APPEAR WHEN FLAP EXTENSION TO 30 DEGS IS ATTEMPTED ABOVE LIMIT SPD.

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WHILE ON ILS RWY 36L AT DFW TRIPPED TRAILING EDGE AND LEADING EDGE FLAP DISAGREE OVER OM; EXECUTED A GAR. RAN TRAILING EDGE FLAP DISAGREE CHKLIST; ALL LIGHTS EXTINGUISHED (LEADING EDGE DISAGREE LIGHTS EXTINGUISHED WITH TRAILING EDGE DISAGREE CHKLIST); LANDED WITH FLAPS 20 DEGS. THE WX WAS 100 AND 1/4 3000 FT RVR; WE HAD APPROX 12.0 FUEL REMAINING. TFC WAS HVY WITH AROUND 3 MI SPACING. WE WERE INSTRUCTED TO MAINTAIN 170 KTS TO THE OM. AT GS INTERCEPT THE FO CALLED FOR FLAPS 30 DEGS; I THEN SELECTED FLAPS 30 DEGS AND NOTICED THE FLAPS HAD STOPPED AT 25 DEGS AND THAT OUR AIRSPD WAS AROUND 165-170 KTS AT WHICH TIME I MOVED THE FLAP LEVER BACK TO 25 DEGS. EITHER I MISSED THE FLAP 25 DEG DETENT OR I WAS MOVING THE HANDLE WHILE THE FLAP RELIEF SYS WAS IN OP. EITHER WAY WE GOT BOTH LEADING EDGE AND TRAILING EDGE FLAP DISAGREE LIGHTS AND EICAS MESSAGES AT WHICH TIME WE EXECUTED A GAR FROM AROUND 1200 FT. WE LEVELED OFF AT 3000 FT; ACCELERATED TO 190 KTS THEN REDUCED BACK TO 170 KTS. DURING THE GAR THE FLAP HANDLE WAS MOVED TO 20 DEG POS OUT OF INSTINCT AND TO SILENCE THE GEAR HORN. BY THE TIME WE RAN THE CHKLIST THE FLAPS WERE INDICATING 20 DEGS AND WE ELECTED TO LAND WITH FLAPS 20 DEGS PER THE CHKLIST. THE FO FLEW THE ACFT WHILE I RAN THE CHKLIST. THE WORKLOAD WAS EXTREMELY HVY WITH ATC INSTRUCTIONS; HVY TFC; BAD WX; FUEL CONSIDERATIONS AND FLYING THE PLANE. AFTER I HAD COMPLETED THE CHKLIST I ASSUMED CTL OF THE ACFT FOR LNDG AND INSTRUCTED THE FO TO REVIEW THE CHKLIST FOR ANY MISTAKES I MIGHT HAVE MADE IN THE HEAT OF THE BATTLE. THERE WAS SOME CONFUSION WITH THE CHKLIST AS TO WHETHER WE COULD RE-EXTEND THE FLAPS TO 30 DEGS WITH ALTERNATE; HOWEVER WE DECIDED NOT TO MOVE THE FLT CTL IN QUESTION NOT BEING EXACTLY SURE WHAT HAD TAKEN PLACE. WE HAD 20 DEG FLAPS; THE RWY WAS 12500 FT LONG; THE WX WAS AT MINIMUMS; WE WERE LOW ON FUEL AND THE TFC WAS HVY; SO WE LANDED UNEVENTFUL. THERE WAS NEVER ANY INDICATION OF FLAP LIMIT ON THE ADI THROUGHOUT THE WHOLE EVENT. AFTER LNDG WE LEFT THE FLAPS AT 20 DEGS FOR MAINT TO INSPECT; ENTERED THE SEQUENCE OF EVENTS IN THE ACFT LOG; AND NOTIFIED A MAINT SUPVR AND MY FLEET SUPVR OF WHAT HAD TAKEN PLACE.