FLC OF AN CPR LEAR JET TOOK EVASIVE ACTION IN RESPONSE TO ANOTHER ACFT APCHING THEIR ALT. NMAC.

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TAXING FOR TKOF FROM OSHKOSH; WI; TO PONTIAC; MI; WITH AN IFR CLRNC OF 'AS FILED; MAINTAIN 3000 FT FOR VECTORS TO MKG; FLT PLAN RTE.' GND CTL ASKED IF WE WOULD PREFER A HIGHER DEP ALT? WE ACKNOWLEDGED; THINKING IT WOULD BE SAFER; HIGHER THAN 3000 FT; HOPING WE WOULD BE ABOVE ANY SMALLER AND SLOWER ACFT THAT WERE ARRIVING AT OSHKOSH. WE WERE RECLRED TO 5000 FT WITH THE REMAINDER OF THE CLRNC TO REMAIN THE SAME. WE WERE CLRED FOR TKOF ON RWY 9; FLY RWY HDG. AFTER TKOF WE SWITCHED TO DEP (GREEN BAY APCH CTL). WE CLBED AT V2 PLUS 15 APPROX 135 KIAS. OUR TCASII WAS ON AND IN THE 10 MI RANGE IN THE ABOVE MODE. AS WE VACATED 2500 FT MSL; THE TCASII ALERTED US OF A TFC ALERT. AFTER GLANCING AT THE TCASII IT ALERTED US THE TFC WAS 500 FT ABOVE US AND TO THE R OF OUR NOSE APPROX THE 1 O'CLOCK POS. LOOKING OUTSIDE TO ASSESS THE SIT; WE FOUND THE TFC; WHICH WAS IN OUR FLT PATH AND TOOK EVASIVE ACTION TO AVOID A COLLISION. WE CONTINUED TO CLB TO OUR ASSIGNED ALT OF 5000 FT. WE ASKED THE CTLR IF HE KNEW OF ANY TFC AT OUR POS. HE REPLIED; YES. THERE IS A BONANZA AT 3000 FT (NBOUND). WE REPLIED; HE WAS AT OUR ALT AS WE WERE CLBING AND WE'RE GOING TO FILE A RPT WITH NASA. WE ACKNOWLEDGED THE TFC AS A 'V' TAIL BONANZA. NOBODY SEEMED TO KNOW OR NOTIFY US OF THE TFC AS WE DEPARTED. WHEN THEY DID TELL US; IT WAS TOO LATE. WE HAD JUST MISSED THE BONANZA; AND THEY TOLD US OF IT AFTER WE RPTED IT. THE TCASII PROVED TO BE A VALUABLE RESOURCE FOR US. HOWEVER AN ACCIDENT COULD; COULD BE AVOIDED WITH BETTER COM BTWN PLTS AND CTLRS. WE RECEIVED A MESSAGE ENRTE TO CALL OSHKOSH TWR AREA MGR. I DID; HE KNEW NOTHING ABOUT IT AND COULD NOT COMMENT ON IT UNTIL HE FOUND OUT MORE INFO.