TCASII DURING CLB. AFTER HDOF BY TWR TO DEP CTLR; AS FLC WAS LEVELING AT SID ALT; DEP CTLR GAVE HDG CLRNC AND CLB. ACFT CLB RATE NOT FAST ENOUGH TO AVOID A TCASII RA. RPTR SAYS; IN ORDER TO LEVEL AT 2000 FT ON SID; THE PWR MUST BE REDUCED AND THEN WHEN COMMENCING CLB IT TAKES A WHILE TO GET CLB RATE BACK.

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AFTER DEPARTING RWY 1 AT TETERBORO; TWR TOLD US WE HAD TFC AHEAD AND TO OUR L AT 1500 FT. I RPTED BACK THAT I DID NOT SEE THE TFC. TWR THEN HANDED US OFF TO DEP CTL. THE SID FOR RWY 1 CALLS FOR A CLB TO 2000 FT. UPON CONTACT WITH DEP CTL WE WERE TOLD 'TURN L TO 270 DEGS; CLB TO 6000 FT.' MY COPLT (THE PF FOR THAT LEG) INITIATED THE TURN AND BEGAN A SLOW CLB. THE CLB RATE WAS INITIALLY SLOW BECAUSE OF THE PWR BEING PULLED SIGNIFICANTLY BACK TO COMPLY WITH THE 2000 FT INITIAL ALT IN THE SID. SHORTLY AFTER THE TURN WAS INITIATED THE TCASII GAVE US A TA. THIS WAS FOLLOWED ALMOST IMMEDIATELY BY AN RA OF 'CLB; CLB; CLB.' AT THE SAME TIME THE TCASII WAS GIVING US THE TA AND THE RA; DEP WAS TALKING TO US. NEITHER OF US COULD UNDERSTAND WHAT DEP WAS TELLING US BECAUSE OF THE TCASII AURAL RA. UPON HEARING THE 'CLB' COMMAND FROM THE TCASII; I IMMEDIATELY INSTRUCTED MY COPLT TO 'INCREASE CLB NOW!!' I WAS LOOKING OUTSIDE TRYING TO FIND THE CONFLICTING TFC. I NEVER SAW THE TFC. AFTER WE WERE CLR OF THE TFC CONFLICT I ASKED DEP TO REPEAT HIS PREVIOUS XMISSION. HE SAID WE HAD A TFC CONFLICT; BUT WE WERE NOW CLR OF TFC. I CAN ONLY GUESS THAT THE TFC RPTED TO US BY TWR WAS THE SAME TFC CONFLICTING WITH US. TO COMPLY WITH AN INITIAL ALT OF ONLY 2000 FT PWR IS SIGNIFICANTLY REDUCED ALMOST IMMEDIATELY AFTER TKOF. WHEN TWR HANDED US OFF TO DEP WE WERE ALREADY LEVEL AT 2000 FT WITH THE PWR WAY BACK. WHEN DEP GAVE US A L TURN AND A CLB; THE TURN WAS IMMEDIATELY INITIATED. AT THE SAME TIME THE PF BEGAN TO GRADUALLY INCREASE THE PWR AND (IN ORDER TO KEEP IT COMFORTABLE AND SMOOTH FOR THE PAX) INITIATE A GRADUAL CLB. BY THIS TIME THE TFC RPTED TO US BY TWR MUST HAVE EITHER BEEN CLBING OR 'STRAYED' CLOSE TO OUR 2000 FT ALT. WHILE CLB RATES AT ALTS BELOW 10000 FT MAY BE AS HIGH AS 5000-7000 FPM FOR MOST JET ACFT; IF THERE IS AN INITIAL LEVELOFF AT A LOWER ALT; ATC SHOULD BE AWARE THAT ONCE GIVEN CLRNC TO CLB IT WILL TAKE SOME TIME TO INCREASE PWR AND RESUME A RAPID CLB RATE.