B737 CREW HAD UNCOMMANDED RUDDER MOVEMENT DURING THE RUDDER FLT CTL CHK. THIS HAPPENED ON 2 SEPARATE ACFT.

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WHILE STOPPED AND AWAITING FOR TAXI CLRNC FROM THE RAMP; I ACCOMPLISHED THE FLT CTL CHK OF THE RUDDER. WHEN THE RUDDER PEDALS WERE RETURNED TO THE NEUTRAL POS; I NOTICED A VIBRATION IN THE AIRFRAME. WITH A TECHNICIAN OUTSIDE THE AIRPLANE OBSERVING THE RUDDER; THE PEDALS WERE DISPLACED. THE TECHNICIAN NOTED THAT WHEN THE RUDDER RETURNED TO CTR; IT WOULD CONTINUE PAST CTR SEVERAL INCHES AND THEN REVERSE DIRECTION. IT WOULD BYPASS CTR; STOP AND REPEAT THE PROCESS. IT WOULD DO THIS SEVERAL TIMES WITH DECREASING FREQUENCY AND AMPLITUDE BEFORE FINALLY STOPPING. I TURNED OFF THE YAW DAMPER; BUT NO CHANGE WAS NOTED WITH THE VIBRATION. APPARENTLY THIS IS WHAT WAS CAUSING THE SHUDDER I FELT IN THE AIRFRAME. MAINT DECIDED TO REMOVE THE ACFT FROM SVC. WE SWAPPED ACFT AND DURING THE FLT CTL CHK ON THE REPLACEMENT ACFT; THE SAME CONDITION NOTED ABOVE WAS OBSERVED. CALLED MAINT AND RETURNED TO THE GATE. FLT WAS CANCELED. AFTER CONSULTING WITH MAINT CTL; APPARENTLY BOEING IS IMPLYING THIS CONDITION IS NORMAL IN SOME OF THE OLDER B737'S AS LONG AS IT DOESN'T OCCUR INFLT. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THAT THE 2 ACFT INVOLVED WERE B737-200'S. THE CAPT ALSO FORWARDED; VIA FAX; A COPY OF A LETTER FROM THE MANUFACTURER TO THE ACR WITH THEIR ASSESSMENT OF THE AIRFRAME VIBRATION INCIDENTS. HE ALSO FAXED TO ASRS THE AIRWORTHINESS DIRECTIVE 97-14-04. THE AIRWORTHINESS DIRECTIVE WAS USED TO CLR THE DISCREPANCY RPTS. AIRWORTHINESS DIRECTIVE 97-14-04 CHKS FOR RUDDER REVERSAL AND ACCORDING TO THE RPTR HAS NOTHING TO DO WITH THE RPTED DISCREPANCY. THE MANUFACTURER ALSO INDICATED IN THEIR WRITTEN RESPONSE TO THE ACR THAT DITHER FOR 3 CYCLES WAS ACCEPTABLE ON THE GND. THE RPTR DESCRIBED EXPERIENCING DITHER FOR 3-5 SECONDS.