G-III FLC DOING MANEUVERS HAS COMMUTER ACFT PASS OVER AND BEHIND IT DURING LEVEL FLT. SECOND ACFT HAS A TCASII ALERT.

Narrative

I DEPARTED TEB ON JUN/THU/96 AT APPROX XX25L IN GULFSTREAM WITH COPLT ON AN IFR FLT PLAN ENRTE TO HOME BASE AT OXC. WE WERE FERRYING AN EMPTY ACFT SUBSEQUENT TO COMPLETION OF CHARTER FLT MDW TO TEB. AFTER CLRING THE NEW YORK CLASS B AIRSPACE N OF THE TAPPAN ZEE BRIDGE; I REQUESTED CANCELLATION OF MY IFR FLT PLAN REQUESTING TO PROCEED VFR TO DEST WITH RADAR ADVISORIES. THIS ACCOMPLISHED; I INFORMED THE CTLR WE WERE CLBING TO 7500 FT MSL FOR A COUPLE OF 'STEEP TURNS.' FO IS NEW ON THE ACFT; AND I DEEMED IT APPROPRIATE TO PROVIDE G-III TRAINING. AT THE COMPLETION OF 2 STEEP TURNS; I DIRECTED A SPD BRAKE DSCNT TO 3500 FT FOR THE REMAINDER OF THE FLT TO DEST. I SO INFORMED THE CTLR; AND HE MENTIONED TFC TO OUR N WHICH I ACKNOWLEDGED AS SEEING. DURING LEVEL FLT AT 3500 FT AN ACFT PASSED OVER AND BEHIND US ON A SOUTHERLY HDG. UPON ARR AT OXC A COMPANY COLLEAGUE; ARRIVING AT HOME BASE IN A HAWKER 700; INFORMED ME A TURBOPROP COMMUTER FLT WAS IN DISCUSSION WITH NEW YORK APCH CTL CONCERNING HIS TCASII PROVIDING HIM AN ALERT. FRIDAY MORNING AN EMPLOYEE OF OXC FBO INFORMED ME THAT AN ARPT EMPLOYEE HAD LEARNED A RPT WAS BEING FILED ON OUR ACFT FOR AN INCIDENT THAT OCCURRED ON THE PREVIOUS EVENING.