JET ACR CREW CLBING FROM FL290 TO FL350 VICINITY OF AIR; OH; RECEIVE TA FROM ZOB CTLR ON TFC AT FL350. CREW STOPPED CLB AT FL345 AND TFC. CTLR BELIEVED HE HAD CLRED THE FLT TO FL330.

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TIME: XA20Z; AUG/XA/98. FLT CLBED (AND CLRED) FROM FL290 TO FL350. CLBING THROUGH APPROX FL340; ATC (ZOB) ISSUED TFC 3 O'CLOCK POS; 5 MI. WE HAD TFC IN SIGHT; STARTED TO QUESTION HIM (ATC) WHEN HE SAID TURN 15 DEGS L; DSND TO FL330. WE STARTED DOWN AT FL340. HE SAID LEVEL AT FL340. WE DID. HE THEN CLRED US TO FL330. HE SAID HE THOUGHT HE HAD ORIGINALLY CLRED US TO FL330; NOT FL350. WE (CAPT AND FO) BOTH HEARD FL350; RESPONDED FL350; AND WERE CLBING TO FL350. TFC NEVER CLOSER THAN 5 MI AND ALSO IN SIGHT. ZOB FREQ. SUPPLEMENTAL INFO FROM ACN 410270. FLT LEFT PHL APPROX XA20Z. WAS CLRED TO CLB FROM FL290 TO FL350 BY ZOB. CREW RESPONDED THAT WE WERE CLRED TO FL350 AND ATC CTLR TOOK NO EXCEPTION. BOTH CAPT AND FO AGREED THEY HAD HEARD FL350 AND SET IT IN ALT WINDOW OF FMC AND BEGAN AUTOPLT CLB. CLBING THROUGH FL340; CTLR RPTED TFC AT 3 O'CLOCK POS; 5 MI. WE RPTED TFC IN SIGHT; BUT HE WAS ALSO AT FL350. WE KNEW THIS WAS WRONG; SINCE WE BOTH COULDN'T BE AT FL350 AND STOPPED OUR CLB AROUND FL345 AND WAITED FOR A BREAK IN THE RADIO TFC TO ASK OUR CTLR WHAT HE REALLY WANTED US TO DO. BEFORE WE COULD ASK; HE SAID HE SHOWED US AT FL345 AND WE RESPONDED YES WE WERE CLRED TO FL350. HE SAID HE THOUGHT HE HAD CLRED US TO FL330. HE ISSUED US A 15 DEG L TURN AND TOLD US TO MAINTAIN FL340. WE MAINTAINED THE OTHER TFC IN SIGHT THE WHOLE TIME AND NEVER GOT CLOSER THAN 5 MI. ATC THEN CLRED US TO FL330. THE REMAINDER OF THE FLT WAS UNEVENTFUL. BOTH CAPT AND FO HAD NO DOUBT WE WERE CLRED TO FL350. WE SUSPECT THAT THE CTLR EITHER MISSPOKE WHEN GIVING US OUR CLRNC OR JUST MADE A MISTAKE AND CLRED US TO A WRONG ALT. THE TAPES SHOULD MAKE THIS CLR.