DC9 FLC DID NOT INTERCEPT STAR RADIAL; AND IN ATTEMPT TO RETURN TO ASSIGNED COURSE; CAME INTO CONFLICT WITH B727 ON ANOTHER CTL FREQ. BOTH ACFT RECEIVED A TCASII RA. THE DC9 FLC DID NOT FOLLOW TCASII RA; WHILE THE B727 DID; FURTHER COMPOUNDING THE SIT. BOTH ACFT SIGHTED THE OTHER; EXECUTING EVASIVE TURNS.

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I WAS THE FO AND PNF ON A NIGHT FLT FROM MDW TO DTW. ZOB WAS CTLING US AND WE HAD BEEN VECTORED FOR TFC. WE WERE LEVEL AT 12000 FT AND THE LAST CLRNC WE RECEIVED WAS TO FLY HDG 090 DEGS TO INTERCEPT THE MIZAR 3 ARR. WE WERE THEN HANDED OFF TO DETROIT APCH CTL. I ATTEMPTED TO CONTACT APCH BUT RECEIVED NO REPLY; THE CTLR WAS BUSY WITH OTHER TFC. AT THIS TIME I BECAME BUSY WITH THE PNF DUTIES. THE CAPT HAD THE 131 DEG RADIAL OFF LFD SET ON HIS HSI AND I HAD THE 246 DEG RADIAL OFF CARLETON SET ON MY HSI. APPARENTLY THE CAPT FLEW THROUGH THE LFD 131 DEG RADIAL TO THE NE SIDE. THE RMI CONFIRMED 20 DEGS APPROX OFF COURSE. THE CAPT MADE AN IMMEDIATE R TURN TO APPROX 160 DEGS TO TRY TO RE-INTERCEPT THE RADIAL. AT THIS TIME I NOTICED THE CRL 246 DEG COME IN AND I CALLED 'COURSE ACTIVE.' THE CAPT BEGAN A SLOW TURN BACK TO THE L BUT WE HAD GONE THROUGH THE CRL 246 DEGS. AT THIS TIME DTW APCH CALLED US SAYING 'SAY HEADING' AND THEN 'TURN L TO HDG 360 DEGS AND DSND TO 11000 FT.' THE CAPT MADE AN IMMEDIATE L TURN AND DSCNT TO 11000 FT. THE CTLR THEN CALLED OUT TFC AT OUR 2 O'CLOCK POS. WE THEN GOT A TCASII TA FOLLOWED IMMEDIATELY BY AN RA WHICH ANNUNCIATED; CLB. WE WERE ALREADY ESTABLISHED IN A HIGH RATE DSCNT SO THE CAPT ELECTED TO FOLLOW THE CTLR'S INSTRUCTIONS. WE LATER LEARNED THAT THE TFC (ACR Y) WAS INITIALLY ALSO AT 12000 FT BUT WAS TALKING TO ZOB AND WAS GIVEN A DSCNT TO 11000 FT BY CLEVELAND. THE RA ENDED WITHIN SECONDS AND THE FLT PROCEEDED NORMALLY TO DTW. SUPPLEMENTAL INFO FROM ACN 405262: I WAS CONCENTRATING SO HARD TO INTERCEPT LFD 131 DEG RADIAL THAT I FLEW THROUGH CRL 246 DEG RADIAL. DECIDED TO FOLLOW CTLR'S DSND COMMAND. DID NOT KNOW THAT CONFLICTING TFC WAS BEING CTLED BY CLE; WHO WAS TELLING THEM TO DSND ALSO. SUPPLEMENTAL INFO FROM ACN 405283: AFTER LEVELOFF; HAD TFC AT 12 O'CLOCK POS 10 MI. TFC STARTED TO CONVERGE. WE RECEIVED THE RA AND STARTED DSCNT TO AVOID. CTLR THEN GAVE DIRECTIONS TO CLB; WE STILL DSNDED; HAD VISUAL ON TFC. TFC DSNDED ALSO AND WAS ON DIFFERENT FREQ. BOTH ACFT TURNED TO THEIR L TO AVOID EACH OTHER.