AN ACR B727 FLC CLBED ABOVE THEIR ASSIGNED ALT WHEN THEY RECEIVED AND READ BACK A CLRNC TO 33000 FT VERSUS THE NEXT SECTOR'S UNDERSTANDING THAT THE ASSIGNMENT WAS 29000 FT.

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AT APPROX XA45Z OUR FLT WAS CLRED DIRECT TO MGW AND CLRED TO FL330. THE FO ACKNOWLEDGED FL330 AND DIRECT MGW. SHE THEN RESET FL330 IN THE ALT ALERTER AND I ANNOUNCED FL330. THIS WAS ON FREQ 127.62 (ZAU). AS WE PROCEEDED RNAV DIRECT MGW OUR FREQ WAS CHANGED TO ZAU 126.32. DURING CLB THROUGH FL300; THE CTLR ASKED WHAT ALT WE WERE CLBING TO. THE FO REPLIED FL330. THIS CTLR STATED WE WERE ONLY CLRED TO FL290. ALL 3 CREW MEMBERS VERIFIED HEARING CLRNC TO FL330 ON THE PREVIOUS FREQ. THE FO XMITTED SHE READ BACK THE CLRNC TO FL330. THE CTLR REPLIED THE COMPUTER HAD ONLY CLRED US TO FL290 -- THERE WAS XING (?) TFC AT FL330; MAINTAIN FL310. WE CONTINUED TO CLB TO AND MAINTAIN FL310. THE CTLR LATER ASKED IF WE STILL REQUESTED FL330; AND WE REPLIED IN THE AFFIRMATIVE. HE LATER STATED THAT TFC WAS NO LONGER A FACTOR; CLB TO AND MAINTAIN FL330. THE QUESTION ABOUT ALT WE WERE CLBING TO FROM THE SECOND CTLR OCCURRED AT APPROX XX51Z (OR SOME 6 MINS AFTER WE HAD ACKNOWLEDGED CLRNC TO FL330 ON THE PREVIOUS SECTOR). I BELIEVE THIS EMPHASIZES CLRNC READBACK; PARTICULARLY AT EVERY CHANCE (PARTICULARLY CHANGING FREQS). IT IS ALSO VERY IMPORTANT FOR ALL CREW MEMBERS TO MONITOR CLRNCS; ESPECIALLY IN THE 'WEE' HRS. I DON'T THINK ALL 3 CREW MEMBERS WOULD HAVE HEARD FL330 OR EXPECTED A STRAIGHT CLB TO REQUESTED ALT; IF IT HAD NOT BEEN RECEIVED. ALTHOUGH NO CONFLICT ACTUALLY OCCURRED; A BUSY SECTOR OR LESS ALERT CTLR COULD HAVE RESULTED IN AN INTRUSION INTO ANOTHER ACFT'S PROTECTED AIRSPACE.