AN ACR LTT CREW MADE A GAR IN RESPONSE TO A TCASII COMMAND.

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OUR FLT WAS ON THE ILS TO RWY 20L AND CLRED FOR THE APCH TO RWY 20L WHEN HANDED US OFF TO TWR ON 128.15. UPON CHKING IN; WE WERE TOLD TO CIRCLE TO RWY 20C AND CONTACT TWR ON 118.6. WE DID SO. THE TWR CLRED US TO LAND ON RWY 20C. ON SHORT FINAL (1/2 - 1/4 MI); WE RECEIVED A TCASII ALERT FOR 'TFC; TFC;' NOT UNUSUAL IN VIEW OF THE FACT THAT SIMULTANEOUS VISUAL APCHS ARE OFTEN DONE ON RWY 20C AND RWY 20R. HOWEVER; WHEN WE RECEIVED AN RA OF 'CLB; CLB; NOW' FROM THE TCASII AND THE TFC ON THE RWY 20R APCH WAS NOT IN SIGHT; AN IMMEDIATE GAR ORDER WAS ISSUED BY MYSELF AND WE DID SO WITH THE PROPER NOTIFICATION TO TWR. SUBSEQUENTLY; WE SHOT ANOTHER APCH TO RWY 20R AND LANDED WITHOUT INCIDENT. GND CTL INSTRUCTED US TO CALL THE TWR WHEN WE WERE PARKED; A JOB THAT I LEFT TO THE PIC. I BELIEVE THAT THE ACFT ON 20R STRAYED L OF COURSE INTO OUR 'SPACE;' AS WE WERE DIRECTLY ON EXTENDED CTRLINE OF RWY 20C AND; HENCE; THE TCASII ALERT. THE WINDS WERE VERY GUSTY FROM THE R. I AM NOT SURE EXACTLY THE DEGREES AND QUANTITY; BUT IT WAS AROUND 15 KTS OF DIRECT XWIND. IN CONCLUSION; I FEEL MYSELF AND MY CAPT VIOLATED NO REGS AND ACTED IN A NOTHING BUT SAFE MANNER WITH COMPLETE THOUGHTS OF SAFETY FOR OURSELVES; OUR ACFT; AND MOST OF ALL OUR PAX IN AVOIDING A VERY POSSIBLE; MAYBE PROBABLE; MIDAIR COLLISION.