ACFT EQUIP PROB - ACR RUDDER TRIM SYS HAD AN UNCOMMANDED FULL L TRIM INPUT DURING CLBOUT.

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I EXPERIENCED A L ACFT YAW AT APPROX 6700 FT MSL. THE ENGS WERE NORMAL AND THE YAW DAMPER WAS TURNED OFF. THE FO NOTICED THAT THE RUDDER TRIM INDICATED FULL L TRIM WITH THE CTL KNOB CTRED. THE FO CTRED THE RUDDER TRIM WHILE I CTLED THE ACFT. WE RETURNED TO ZZZ AND MADE AN UNEVENTFUL LNDG. CALLBACK CONVERSATION WITH REPORTER REVEALED THE FOLLOWING: THE CAPT WAS HAND FLYING THE ACFT DURING THE CLB OUT. AT 6700 FT MSL HE FOUND THAT HE HAD TO PUSH SOME RUDDER IN ON THE R PEDAL TO KEEP THE ACFT GOING STRAIGHT. HE CHKED THE ENGS AND THEY WERE PRODUCING BALANCED PWR SO HE TOLD THE FO ABOUT THE PROB AND REQUESTED A LEVEL OFF AT 7000 FT. WHILE THEY WERE LEVEL THEY STARTED AN ANALYSIS OF THE PROB. THE FO VERIFIED THAT THE ENGS; FLT CTLS AND FUEL WERE IN A BALANCED CONDITION AND TURNED OFF THE YAW DAMPER AS PER PROC. THE FLC DISCUSSED TURNING OFF THE HYD PWR TO THE FLT CTLS; BUT DECIDED NOT TO DO THAT. A FEW SECONDS LATER THE FO NOTICED THE RUDDER TRIM WAS FULLY DEFLECTED TO THE L AND WITH THE CAPT'S CONCURRENCE SLOWLY CTRED IT. THE FLC DECIDED TO RETURN AND LAND. MAINT DECIDED TO REMOVE THE ENTIRE RUDDER TRIM MECHANISM FROM THE ACFT FOR A DETAILED EXAMINATION. THE FLC HAS BEEN INTERVIEWED BY A NUMBER OF DIFFERENT PEOPLE FROM SEVERAL ORGANIZATIONS AND THE EQUIP TESTING IS ONGOING. A B737-400 CAPT FOR ANOTHER ACR WAS ON BOARD AND HE RPTED THAT THE YAW MOVEMENT WAS VERY NOTICEABLE TO HIM AND THE PAX. THE FLT ATTENDANTS WERE INFORMED OF THE SIT BY THE FLC AS SOON AS THEY HAD THE ACFT UNDER CTL AND THE ATTENDANTS ALSO RPTED THE NOTICEABLE YAW. THE NOTICEABLE YAW OCCURRED DURING PWR REDUCTION AFTER LEVELING AT 7000 FT. THE CAPT ATTEMPTED TO BRING THE THROTTLES BACK SMOOTHLY TOGETHER WHILE ADJUSTING HIS RUDDER INPUTS TO THE NEW FLT DYNAMICS FOR THE B737-300; BUT ADMITTED THAT HE COULD HAVE BEEN MORE PRECISE WITH PRACTICE IN THIS CONFIGN.