ACR X TCASII RA DSCNT HAD LTSS FROM ACR Y. NON ADHERENCE TO ATC CLRNC. EVASIVE ACTION TAKEN.

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ACR X WAS BEING VECTORED FOR A L DOWNWIND FOR RWY 21L AT DTW. HE WAS LEVEL AT 11000 FT. ACR Y WAS CLBING TO 10000 FT EBOUND (120 DEG HDG) OFF OF DTW (ACR Y WAS NOT TCASII EQUIPPED). ACR X BEGAN A DSCNT; ESTABLISHED ON A 300 DEG HDG; HEAD ON WITH ACR Y CLBING OUT OF 9400 FT FOR 10000 FT. HE ADVISED ME HE HAD GOTTEN AN RA AND WAS DSNDING. HE WAS THEN OUT OF 10700 FT. I IMMEDIATELY TOLD ACR X TO 'NOT DSND; THE OTHER ACFT WAS CLBING TO 10000 FT.' IT APPEARED THEN THAT ACR X WAS PASSING BEHIND ACR Y AT 10700 FT. ACR Y WAS AT 10000 FT. HE THEN BEGAN A CLB TO 11200 ST. THIS WAS VERY UPSETTING FIRST BECAUSE I HAD NOT SEEN A DSCNT RA INTO A CLBING ACFT BEFORE. ONLY ONCE WHEN TCASII WAS VERY NEW. THIS COULD HAVE BEEN DISASTROUS. ACR Y; NOT HAVING TCASII; HAD NO IDEA OF THIS SIT AND WAS GOING TO LEVEL AT 10000 FT. MEANWHILE ACR X IS DSNDING INTO HIS PROTECTED AIRSPACE. THIS IS A CTLED ENVIRONMENT WHERE CLBING AND DSNDING ACFT ARE SEPARATED BY 1000 FT. THERE SHOULD BE SOME LIMITS TO THE MANEUVERS EXECUTED IN REGARD TO THE RA; WHEN IN A TCA; IN CLOSE PROX TO THE ARPT. THIS WAS JUST A LITTLE TOO CLOSE FOR MY COMFORT. I TRUST THE SYS AND RELY ON THE PLTS TO DO WHAT I DIRECT. I LOSE FAITH IN THE SYS WHEN THE PLTS CAN MAKE SUCH DRASTIC DEVS FROM THEIR ASSIGNED ALTS AND TELL US AFTER THE FACT.