A B757-200's numbers one and four autobrakes malfunctioned on landing causing the tires to flatten. Steering difficulty was overcome on the runway after landing and the aircraft was taxied to the gate.

Narrative

We experienced two blown tires on the left truck due to an anti-skid module failure. A landing was thoroughly briefed by the First Officer. Autobrakes 3 was used to facilitate a timely application of braking and minimize the landing roll on the wet runway (there was no standing water and it was not currently raining).The aircraft weight was approximately 193;000 LBS with a resultant Vref of 130 plus 5 KTS to make a target speed of 135 KTS. The approach was normal with no noticeable deviations from the plan. A landing was accomplished approximately 1000 FT beyond the threshold at approximately the target speed. The spoilers deployed normally and reverse thrust was employed expeditiously. I began normal to moderate manually braking shortly after touchdown. The braking felt normal down to approximately 60 KTS. The reversers were stowed by about 70 KTS. Beginning at approximately 60 KTS as pedal pressure was increased to attempt exiting at intersection A1 the left brake started to feel 'spongy' and it felt like the left side wheels were skidding and the aircraft began to swerve to the right. All brake pedal pressure was lessened to stop the divergence and release the perceived skid. Braking was again attempted with similar results except I applied aggressive left rudder to attempt to keep the aircraft on the centerline but again the aircraft swerved right. I again released and reapplied brake pressure with similar results. The aircraft was continuing to decelerate throughout these braking attempts but just not as desired nor as would be normal. I was unable to exit as planned at A1. I passed control of the aircraft to the Captain to see if she could better stop the aircraft thinking that possibly her brake pedals might better respond to inputs plus she would have the tiller authority if necessary to counteract any planned runway track divergence. She had braking results similar to mine. She did manage to slow the aircraft and exit by taxiway E. We both agreed the braking did not feel normal and the left brake pedal felt 'spongy'. During taxi in the Captain ascertain that sufficient braking authority existed for a safe albeit slow taxi to the gate. The aircraft felt normal during the taxi (no vibration or shudder). The aircraft seemed to respond normally to thrust inputs and excessive thrust was not required to taxi. The perceived braking deficiency was reported verbally and via ACARS to maintenance. Post flight inspection revealed the #1 and #4 tires had been blown. The tires were totally flattened through all cord layers in one area as the tires obviously were skidding without release.