B737-300 ACFT IN CRUISE HAD DIFFICULTY WITH STABILIZER TRIM. EVEN ELECTRIC TRIM WOULD NOT CTL IT NOR MANUAL. FLC COULD NOT TRIM NOSE DOWN. AFTER COORD WITH COMPANY MAINT FLC DECLARED EMER AND DIVERTED. LNDG WAS UNEVENTFUL AND; THOUGH THE STABILIZER WAS COMPLETELY JAMMED; FLC HAD NO DIFFICULTY CTLING THE ACFT FOR APCH AND LNDG.

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ACFT WAS LEVEL AT FL330; .74 MACH ON AUTOPLT USING VNAV AND LNAV. AT APPROX XA00Z; CAPT RETURNED TO COCKPIT AFTER USING LAVATORY FACILITIES. FO WAS EXPERIENCING DIFFICULTY HOLDING ALT. TRIED USING VERT SPD CTL BUT WAS INEFFECTIVE. CAPT ASSUMED CTL OF ACFT AND TRIED TO LEVEL OFF ACFT USING VERT SPD -- STILL INEFFECTIVE. AUTOPLT DISENGAGED AND ACFT FLOWN MANUALLY TO ALT; HOWEVER; WHEN ELECTRIC TRIM WAS USED; NOTHING HAPPENED. CIRCUIT BREAKERS WERE CHKED IN. MANUAL STABILIZER TRIM WAS TRIED NEXT BUT TRIM WHEEL WAS JAMMED (COULD NOT TRIM NOSE DOWN). SYS MAINT WAS CONTACTED AND WITH THEIR GUIDANCE PROCEEDED TO TROUBLESHOOT SYS. NOTHING SEEMED TO WORK. 'NOSE UP' TRIM WORKED BUT ONCE NEW POS WAS REACHED COULD NOT TRIM 'NOSE DOWN.' DECLARED AN EMER AND DIVERTED TO PREPLANNED ALTERNATE FIELD (BNA). ALL OTHER SUITABLE ARPTS WERE EXPERIENCING HVY WX. BNA HAD THE BEST WX AND THE LONGEST RWY. PROCEEDED TO BNA WHILE STILL TALKING TO MAINT AND CHICAGO DISPATCH TO CONSIDER ALL OPTIONS. CABIN CREW NOTIFIED OF SIT AND WERE INSTRUCTED TO 'PREP' THE CABIN FOR EMER LNDG AND POSSIBLE EVAC. UPON DSCNT INTO BNA; ACFT WAS LEVELED AT 6000 FT TO DO A CTLABILITY CHK. ONCE FLAPS WERE EXTENDED TO 10 DEGS DOWN AND LNDG GEAR POSITIONED DOWN; LOST ALL STABILIZER TRIM (BOTH NOSE UP AND NOSE DOWN). ELEVATOR CTL WAS ADEQUATE TO CONDUCT APCH. 'JAMMED STABILIZER APCH' EMER PROCS WERE FOLLOWED. A 15 DEG FLAP LNDG WAS UTILIZED. EXTENDED STRAIGHT-IN APCH WAS USED. LNDG WAS UNEVENTFUL. CRASH CREW CHKED FOR HOT BRAKES AFTER EXITING RWY. NO INJURIES OR DAMAGE TO THE ACFT OCCURRED. ALL CREW MEMBERS CONDUCTED THEMSELVES IN A HIGHLY PROFESSIONAL MANNER. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: RPTR CAPT CONFIRMED ACFT TYPE AS B737-300. HE HAD NOT RECEIVED FEEDBACK FROM HIS COMPANY YET; BUT WOULD GET IT. WHEN TALKING WITH HIS COMPANY MAINT THEY MENTIONED SOMETHING ABOUT A GEAR BOX AND JACKSCREW PROBABLY CAUSING THE PROB. AS SOON AS THEY LANDED THEY WERE QUESTIONED BY THE FAA REGARDING THE TRIM PROB.