On January 8, 2008, about 1745 central standard time, N733TW, a Boeing 737-2H4, operated by Ameristar Air Cargo, Inc., sustained no damage when it lost directional control and exited the taxiway while taxiing from landing at the Lincoln Airport (LNK), near Lincoln, Nebraska. The non-scheduled domestic passenger flight was operating under 14 CFR Part 121. The airline transport rated pilot and co-pilot, 4 flight attendants, 1 jump seat occupant, and 31 passengers were uninjured after deplaning via the airplane's airstairs. Visual meteorological conditions prevailed at the time of the accident. The flight originated about 1559 from the Austin-Bergstrom International Airport, near Austin, Texas, and was destined for LNK. The operator reported that on January 6, 2008, the airplane was in maintenance for a "[Left/Hand Main Landing Gear] swivel valve leaking." The corrective action was accomplished by one of the operator's mechanics. The mechanic reportedly removed both the swivel valves on the left main landing gear. The aft swivel valve was removed and replaced with a new valve. The forward one was removed and reinstalled. That maintenance was checked for leaks and the airplane was returned to service. The airplane's maintenance manual 32-41-61 contained a warning that stated: WARNING: MAKE SURE THAT THE SWIVEL JOINT AND HYDRAULIC LINES ARE ORIENTED AS SHOWN ... . THE HYDRAULIC LINE TO THE BRAKE ASSEMBLY MUST BE CONNECTED TO THE SWIVEL HOUSING AND THE HYDRAULIC LINE FROM THE ANTI-SKID VALVE TO THE SWIVEL FITTING AS SHOWN ... . IF THE ASSEMBLY OF THE SWIVEL AND THE HYDRAULIC LINES ARE ROTATED 180 DEGREES, THE HYDRAULIC LINES CAN BE CONNECTED BUT THE SWIVEL WILL NOT OPERATE. THIS CAN CAUSE THE HYDRAULIC LINES TO BREAK DURING EXTENSION AND RETRACTION AND CAUSE THE BRAKES PRESSURE TO BE LOST. The captain, in part, stated: At about 12 miles from the airport with runway 36 insight and the airspeed at 210 knots started extending the flaps on schedule. When lowering the gear we performed the Before Landing Checklist and observed all systems normal upon completing the checklist and the flaps at 30 degrees. I landed on runway 36 in Lincoln, NE (LNK) with all systems normal and exited taxiway Juliet to the right per tower instructions. As I exited runway 36 I then stowed the speed brakes and called for the after landing checklist. ... While taxiing to parking ... the Master Caution "HYD" Light illuminated followed by an immediate loss of System "B" Hydraulics. I immediately started trying to get the airplane stopped and observed no braking and no response to tiller movement for nose wheel steering. I then tried to deploy the thrust reversers and couldn't get the [thrust reverser]'s to deploy. Within a few seconds after the loss of System B, we observed that a total loss of System "A" Hydraulics had occurred as well. In this very short time period the airplane started a slight turn to the left. I was applying the right rudder with no response in the steering. I then asked for assistance from [the] First Officer ... with the right rudder. The [a]irplane exited the taxiway to the left into the mud and snow. After coordinating with fire and rescue, I made the decision to use the aircraft stairs to deplane the passengers. Examination of the swivel valves after the incident revealed that both valves were not installed as depicted in the maintenance manual.