A B727 FLC HAD AN NMAC NEAR CCC.

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WE WERE TOLD BY CTR; ABOVE 10000 FT; TO MAINTAIN 250 KTS. WE DID. WE WERE IN THE CLBOUT; AND ZBW CLRED US UP TO FL230. ALL 3 OF US (CREW) HEARD IT. THE FO REPEATED THE CLRNC BACK TO ATC ('UP TO 230'). FO POINTED TO THE ALT ALERTER; AND I SAID OUT LOUD; 'FL230.' JUST OUT OF FL200; WE HEARD ACFT Y TELL ATC 'THERE IS A JET CLBING AT US.' I LOOKED CAREFULLY OUT THE FRONT WINDOW; SAW IT WAS THEM. I IMMEDIATELY CHOPPED THE PWR AND LEVELED OFF AT FL204. I BELIEVE THEY WENT BY AT FL210 WITHIN 2 MI. THEY DID NOT DEVIATE. WE WERE THE ONES WHO SLOWED OUR CLB AND LEVELED OFF. ATC WAS TOTALLY 'OUT OF THE LOOP.' I GUESS NO ALARMS WENT OFF AT ATC. ACFT Y THANKFULLY SAW US ON TCASII AND SAID SOMETHING. ATC THEN (HE RESPONDED (ATC) VERY SLOWLY -- KNOWING HE MESSED UP) ASKED WHAT ALT WE WERE CLRED TO. WE SAID 'FL230.' SO THEN WE WERE AT FL204; AND ATC (GUESSED SHOOK UP) WOULDN'T SAY WHAT ALT TO GO TO. I TOLD FO; 'ASK HIM WHAT ALT DOES HE WANT US TO GO TO.' HE ASKED. ATC TOOK A LONG TIME TO RESPOND. THEN HE SAID; 'CLB TO FL230.' THE FO READ IT BACK AND POINTED TO THE NEW ALT. I SAID IT OUT LOUD. THEN WE CLBED TO FL230. THEY FINALLY; AFTER WE ASKED; GOT TO GO TO NORMAL AIRSPD. REST OF FLT WENT FINE. IT IS TIME CARGO JETS NEED TCASII!