A CLBING S80 CLRED TO 10000 FT IS TOLD TO LEVEL AT 7000 FT AS THEY PASSED THAT ALT E OF TTT; TX.

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TTT 094 DEG RADIAL; 10 DME. FO FLYING DEP. AT 7000 FT; DEP CTL ASKED US TO LEVEL OFF AT 7000 FT. WE WERE CLBING AT ABOUT 4000 FPM. I EASED THE NOSE OVER AND LEVELED OFF AT 7500 FT. I THEN RECEIVED AN RA TO MONITOR VERT SPD. THE CTLR HAD DIRECTED 7000 FT BUT THE TCASII WANTED LEVEL TO CLBING ACTION. THE CAPT HAD THE ACFT IN SIGHT. I REMAINED AT 7500 FT. THE CTLR THEN DIRECTED A CLB TO 17000 FT. I BELIEVE THAT DUE TO OUR RATE OF CLB THE RADAR SCOPE WAS NOT KEEPING UP WITH US AND THE CTLR ATTEMPTED TO KEEP US BELOW THE TFC. SUPPLEMENTAL INFO FROM ACN 452221: DURING DEP CLBOUT WITH CLRNC TO 10000 FT; WE LEVELED AT 7500 FT; QUERIED CTLR; THEN GOT A TCASII FOR CLB. I SAW TFC AT 11 O'CLOCK POS; 5 MI OUT WITH LIGHTS ON. WE CONTINUED CLB WITH CLRNC TO 17000 FT. I AGAIN ASKED FEMALE CTLR AND SAID WE HAD A TCASII ALERT WHICH WE FOLLOWED. SHE SAID IT WAS HER ERROR AS SHE FORGOT ABOUT THE TFC CAUSING OUR 7000 FT LEVELOFF CALL. I STATED WE WERE ALREADY THROUGH 7000 FT AND THAT THERE WAS NO WAY TO LEVEL AT 7000 FT WITH THAT CLB RATE. SHE REITERATED IT WAS HER ERROR. FO DID A GOOD JOB OF HANDLING SIT.