What was found
DURING CRUISE AT FL370, AUTOPILOT ENGAGED, THE STABILIZER OUT OF TRIM LIGHT ILLUMINATED. CHECKLIST PROCEDURES WERE FOLLOWED AND AUTOPILOT DISENGAGED TO RETRIM AIRCRAFT. THE ELECTRIC TRIM IN THE NOSE UP POSITION WOULD NOT WORK AND MANUAL TRIMMING WAS HARDER THAN NORMAL AND FELT LIKE IT WAS BINDING. NOSE DOWN TRIM WORKED NORMALLY IN BOTH ELECTRIC AND MANUAL MODES. AN EMERGENCY WAS DECLARED AND AIRCRAFT DIVERTED TO AND LANDED AT DFW WITHOUT INCIDENT. REMOVED AND REPLACED THE UP STABILIZER SWITCH. GROUND OPERATIONAL CHECK NORMAL.