A B747 FLT CREW WHILE TAXIING; LOSES ACFT CTL AND ENDS UP STUCK IN THE MUD ON THE SIDE OF THE TXWY.

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FO MADE NORMAL APCH AND LNDG. WE PREBRIEFED HIM TO MAKE TURNOFF OF ACTIVE ONTO TXWY M THEN ONTO TXWY E. AS ACFT WAS NEBOUND ON TXWY E; AS I WAS ASSUMING CTL OF THE TILLER; ACFT WAS DRIFTING R OF TXWY CTRLINE. I ASSUMED CTL AND INPUTTED A L-HAND STEERING COMMAND. ACFT WAS UNUSUALLY SLUGGISH TO RESPOND; SO I INPUTTED A FURTHER L-HAND COMMAND AT WHICH TIME THE ACFT SUDDENLY SWERVED TO L AND DRIFTED ACROSS THE CTRLINE OF TXWY E; AND BEGAN HEADING TO THE L EDGE OF THE TXWY. I IMMEDIATELY ADDED ADDITIONAL 4-HAND STEERING INPUT FROM WHAT I HAD INPUTTED TO CORRECT BACK TO CTRLINE BUT; AGAIN; ACFT WAS SLOW TO RESPOND AND DRIFTED OFF THE EDGE OF THE TXWY WITH THE L-HAND WING GEAR AND NOSE GEAR COMING TO REST IN SOFT EARTH. ALL BRAKING AND STEERING INPUTS TO KEEP ACFT ON TXWY SEEMED TO HAVE LITTLE OR NO EFFECT. WHEN I REALIZED ACFT WAS MIRED IN THE SOFT EARTH WITH NO FIRE OR OTHER EMERS APPARENT; I ORDERED THE FO TO CALL THE CABIN AND TELL EVERYONE TO REMAIN SEATED; WHICH HE DID. NO EVAC TOOK PLACE. WE COORDINATED WITH GND CTL TO GET CFR TO THE SCENE WHICH WAS ACCOMPLISHED IN A TIMELY MANNER. PAX AND CREW WERE THEN DEPLANED THROUGH DOOR 1R VIA MOBILE STAIRS AND BUSSED TO THE TERMINAL. COCKPIT WAS SECURED USING NORMAL SHUTDOWN/PARKING CHKLISTS AND COMPANY WAS NOTIFIED. ACFT WAS PREVENTED FROM SLIDING OVER A LARGE EMBANKMENT TO THE R OF TXWY E.