B757-200 flight crew encounters leading and trailing edge flap anomalies on final approach. Minimum fuel situation complicates completing complex QRH procedures in a timely fashion. Land with flaps 1 degree.

Narrative

The last leg of a 3-day trip; and it was the First Officer's leg. We were right base to ZZZ Runway XX; which is the longest runway. At 210 KTS; First Officer called 'below 240 KIAS; Flaps 1 degree.' In doing so; we received an EICAS message; 'Leading Edge Slat Disagreement' and a leading edge light. The flap indicator was less than 1 degree. We got vectors to a right-hand box pattern at 4000 FT MSL to ILS final to Runway XX. An emergency was declared with Approach with ARFF requested. We ran the QRH checklists and before landing checklists. A second 360 degree turn was requested on final to complete the checklists. We stayed on final; due to our low fuel state. The planned arrival fuel at ZZZ was 7.7 with no alternate. We accomplished the 757 Leading Edge Slat Disagreement checklist. Upon completing the bullet 'if; after selecting 'alternate' the leading edge light remains illuminated' (and it did not stay illuminated) we accomplished the next step: Alternate Flap Selector -- set extend or retract flaps as required. Upon selecting Alternate Flap Selector to 5 degrees; we received a Trailing Edge Flap Disagreement EICAS message and trailing edge light. We accomplished the 757 Trail Edge Flap disagreement QRH checklist. After leading edge and trailing edge alternate flap switches 'alternate.' If; after selecting 'alternate' the trailing edge light remains illuminated (and it did remain illuminated); Trailing Edge Alternate Flaps switch -- off. We accomplished the 757 Trailing Edge Flap Asymmetrical checklist. We accomplished 'if indicated flap position at or between 1 and 5; use current flaps and Vref 30+40 for landing.' The #1 Flight Attendant was briefed via interphone on final approach that I had a flap problem; and we would be landing at a fast speed. I told them I did not plan an evacuation and they would see fire trucks on rollout. I told them to watch and expect me to communicate if there were further instructions after landing. I took control of the aircraft on final approach and landed the aircraft on centerline in the landing zone at 167 KIAS. Aircraft weight was 181.5 upon landing and in fuel 3.9. Flap indicator and flap handle were at 1 degree for landing; Autobrakes 3. After stopping was assured; manual braking was used to use the entire runway length. After clearing the runway; I stopped for the Fire Chief to inspect for any abnormality; smoke; hot brakes; tire problems; or leaks. The Fire Chief said everything looked OK. As a precaution; we kept ramp personnel away from the aircraft until maintenance cleared the brakes and tires. The Mechanic said the brakes and tires were fine and the brakes were then set for parking. The Mechanic brought up the flap handle in the chocks with no results. He retracted the flaps with the alternate system. The voice recorder CB was pulled. I wrote up the flaps in the aircraft logbook to the best of my knowledge and debriefed the Mechanic. All checklists were accomplished under extreme time constraints of low fuel. Checklists could be written better in regards to bullets; indentations and content because this checklist can be run in a landing scenario where fuel is a factor.