C550 CREW RECEIVES 2 TCASII TFC ALERTS WHILE CLBING IN PHX CLASS B AIRSPACE.

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WE DEPARTED RWY 21 AT SDL; CLRED FOR A R TURN TO 300 DEG HDG FOR THE BONYO 3 DEP; DRAKE TRANSITION CLB TO 5000 FT. AT 4200 FT; WE WERE GIVEN TFC AT 4500 FT; AND TOLD WE HAD A TFC CONFLICT. WE WERE CLBING AT 2500 FPM. CAPT PULLED BACK TO CLB THROUGH 4500 FT AS WE WOULD NOT BE ABLE TO ARREST CLB QUICK ENOUGH. OUR TCASII CALLED OUT 'TFC; TFC.' WE NEVER SAW TFC UNTIL WE WERE AT 5000 FT; AND TURNING TO THE R. JUST AFTER THAT WE WERE CLRED TO 6000 FT; AND SWITCHED TO ANOTHER FREQ AND CLRED DIRECT BONYO. APCHING 6000 FT; OUR TCASII SOUNDED 'TFC; TFC.' WE NEVER SAW THIS ACFT. WHEN WE LEVELED AT 6000 FT; THE TCASII SHOWED IT 800 FT BELOW US. WE WERE SOON GIVEN A HIGHER ALT AND HANDED OFF TO ZAB WITH NO MENTION OF WHAT HAPPENED. THE FIRST AND MOST CRITICAL TFC CONFLICT WAS IN RADIO CONTACT WITH THE SAME CTLR WE WERE. THE FREQ WAS VERY CONGESTED AND IT TOOK UNTIL 3500 FT TO GET OUR INITIAL RADIO CALL IN. THIS PROBABLY IS WHY THE CTLR DID NOT WARN EITHER AIRPLANE SOONER; ALTHOUGH IT SEEMS THAT SOMETHING SHOULD HAVE BEEN DONE BY THE CTLR SOONER.