FLC OF CPR LTT ON INITIAL CLB DISCOVERS NOSE GEAR WILL NOT RETRACT. DURING VECTORS FOR RETURN THEY MISINTERP CLB CLRNC AND EXCEED ASSIGNED ALT BY 600 FT.

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AFTER TKOF FROM TEB; FO FLYING CALLED FOR GEAR UP AND I (THE CAPT) SELECTED GEAR UP; HOWEVER THE NOSE GEAR DID NOT RETRACT. I ADVISED TEB TWR WE WOULD LIKE TO RETURN FOR A LNDG AT TEB. THEY ADVISED ME TO CONTACT DEP. I CONTACTED DE;P ADVISING WE HAD A SLIGHT PROB AND WOULD LIKE TO RETURN TO TEB AND NO ASSISTANCE WAS REQUIRED. WE WERE TOLD TO TURN TO A HDG OF 270 DEGS AND MAINTAIN 1500 FT AGL. WE WERE PASSED TO ANOTHER FREQ AND TOLD TO MAINTAIN A NEW HDG (320 DEGS I THINK) AND MAINTAIN 4000 FT; WHICH WE READ BACK. GOING THROUGH 3600 FT; WE WERE ADVISED WE WERE ONLY CLRED TO 3000 FT AND WERE INSTRUCTED TO DSND TO 3000 FT AGL; AND WE DID IMMEDIATELY. I QUESTIONED MY FO AND HE WAS CERTAIN ALSO WE WERE CLRED TO 4000 FT. ATC WAS QUITE BUSY AND WE WERE QUITE BUSY DOING AFTER TKOF CHKS; BEFORE LNDG CHKS; GETTING APCH PLATES OUT AND DEALING WITH THE LNDG GEAR PROB. I FELT THE WORKLOAD IN THE COCKPIT WAS QUITE HIGH AND IT IS POSSIBLE THAT A WRONG ALT WAS HEARD AND READ BACK. AS FAR AS I KNOW THERE WAS NO CONFLICT INVOLVED WITH ANY OTHER ACFT.