ALTDEV ALT EXCURSION DURING TCASII RA.

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FLT FROM BUF TO DCA; A B737-300. CREW OF 5; 22 PAX. WE WERE INBOUND TO DCA VOR ON COURSE 230 DEGS; AT 300 KTS; LEVEL AT 10000 FT. VFR CONDITIONS. IN CONTACT WITH DCA APCH CTL 124.2. CLRNC WAS 'DIRECT TO VOR; MAINTAIN 10000 FT.' 10 MI SW OF BWI; OUR TCASII EMITTED AURAL AND INSTRUMENTAL WARNING 'DON'T CLB.' THREAT TARGET ON OUR DISPLAY WAS AT 1 O'CLOCK POS AND RED. 1 OR 2 SECONDS LATER; TCASII COMMANDED 'DSND' WITH THE VSI SHOWING RED IN THE CLB SECTION AND GREEN DOTS IN THE DSCNT SECTION. MY FO SAW AN ACFT BELOW US AT 8000 FT OR 9000 FT; AND DELAYED LEAVING 10000 FT MOMENTARILY. TCASII THEN COMMANDED 'INCREASE DSCNT.' I ORDERED THE FO TO COMPLY; AND NOTIFIED ATC THAT WE WERE OUT OF 10000 FT TO COMPLY WITH TCASII. TCASII ALERT STOPPED WHEN WE WERE AT 9200 FT AND THE ACFT BELOW US AT OUR 1O O'CLOCK POS; BELOW US; AND MOVING AWAY. NORMAL APCH AND LNDG ACCOMPLISHED AT DCA. AFTER LNDG; CALLED DCA ATC. THEY INDICATED THAT SEPARATION WAS NOT LOST WITH ACFT BELOW US AND THERE WAS NO ACFT ABOVE US EXCEPT FOR ONE AT 13000 FT AND LEVEL. ASSISTANT CHIEF PLT BWI CALLED BWI APCH CTL. BWI ATC RELAYED TO HIM THAT AN MD-80 CLBING FROM BWI; CLRED TO 8000 FT; WAS CLBING SO FAST THAT OUR TCASII INTERPRETED IT AS A THREAT THROUGH OUR ALT. I BELIEVE THE MD-80 TCASII WAS TELLING THEM TO 'CLB' AND WITH OURS TELLING US TO 'DSND.' WELL; A POTENTIAL; VERY BAD SIT MIGHT HAVE HAPPENED. FORTUNATELY; MY FO SAW THIS ACFT BELOW US AND AVERTED A CLOSE CALL. OUR TRAINING WITH THE TCASII UNIT SPECIFIED THAT WE ARE TO COMPLY WITH TCASII CONFLICT WARNINGS UNLESS OR UNTIL POSITIVE VISUAL CONTACT WITH THE INTRUDER PROVIDES A CORRECTIVE COURSE OF ACTION. IT WAS LOOKING UP FOR AN INTRUDER THAT WASN'T THERE AND IT WAS MY FO WHO WAS ABLE TO TAKE THE CORRECT ACTION. BWI ATC INDICATED THAT THIS PROB WITH BWI DEPS SETTING OFF FALSE TCASII WARNINGS FOR DCA ACFT HAS HAPPENED BEFORE. I MIGHT ADD IN CLOSING; THAT THIS WHOLE INCIDENT TOOK PLACE IN ABOUT 15 SECONDS TIME.