A B757 FLT CREW RECEIVES A TCASII TA-RA FROM AN F100 WHILE ON APCH AT DFW.

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ON JUL/FRI/03; OUR B757 WAS ON A VISUAL APCH TO RWY 18R AT DFW WITH CHK AIRMAN FLYING FROM THE R SEAT. APCH WARNED US OF TFC AT OUR L 10 O'CLOCK POS SLIGHTLY LOW APCHING. OUR TCASII IDENTED THE TFC IN THE SAME SPOT. I BEGAN SEARCHING FOR THE TFC WHILE HELPING PIC CONFIGURE OUR JET. WHEN I SAW THE F100; HE WAS IN A HARD L TURN SHOWING ME HIS BELLY AND APCHING US RAPIDLY. OUR TCASII ISSUED A TA FOLLOWED QUICKLY BY AN RA. I TOLD THE CHK AIRMAN TO STOP DSNDING; DO NOT DSND ANYMORE AND PREPARED TO TAKE THE CTLS. THE F100; WHO APPARENTLY WAS ON APCH TO AN E SIDE RWY; CAME WITHIN ABOUT 300 FT OF US. AT ONE POINT I THOUGHT HE WAS GOING TO GO UNDER US AT WHICH POINT I WOULD HAVE TAKEN CTL OF OUR B757. THE F100 FINALLY GOT ENOUGH L TURN IN TO START OPENING UP SOME SPACING ON US; AND I DIRECTED CHK AIRMAN TO RESUME HIS DSCNT. AT THE SAME TIME WE WERE SWITCHED TO TWR AND AFTER TAKING A DEEP BREATH; I CHKED IN; REMARKED ON THE F100; AND RECEIVED LNDG CLRNC. DURING THE ENTIRE EXERCISE; ATC PROVIDED INFO AND WARNINGS; AND; A CTLR ON THE ATC HOTLINE IN OPS GAVE ME ALL THE DETAILS AND EXPLANATION FROM HIS END THAT I NEEDED. THE F100 APPARENTLY WAS LOOKING AT THE W SIDE RWYS WHEN THEY WERE CLRED TO AN E SIDE RWY. BY THE GRACE OF GOD; AND WITH HELP FROM ATC AND TCASII; WE CAME NO CLOSER THAN 300 FT; 'MY ESTIMATE.' NONE OF MY PAX REMARKED ABOUT THIS INCIDENT WHEN WE SAID GOODBYE AT THE DOOR.