Medium Transport
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown
Conflict NMAC
Flight Crew Took Evasive Action
Procedure; Airspace Structure
We received a double RA when climbing through 17;000 from ECP airport towards the HEVVN Intersection. We were provided a climb to FL230. At around 16;500 feet we were given a frequency change to ZJX center (I think a military controller was working us). During the handoff our TCAS went off and a plane was coming right at us. He was at 17;500. We were climbing through 17;000. I quickly asked the controller if he has traffic for us before I changed frequencies and he then gave us a traffic alert but by this point our TCAS went to an RA for us to descend. We complied and I advised ATC but the intruder plane now started a descent. I saw his red TCAS Symbol say '0' feet difference with a red down arrow and he was coming right at us. Our TCAS then changed and said 'CLIMB! CLIMB NOW! CLIMB NOW!' My partner complied. At this point I picked the plane up visually. It appeared to be an eclipse jet. He obviously saw us and was nose down and banked to the right trying to avoid us. He passed us at approximately our altitude and within 500 feet to our left. Our closer speed with him was probably over 600 knots and it was quite a sight seeing him go zipping by us. I then spoke to ATC slightly agitated and asked again; did he have this traffic for us. He wasn't working this jet and it was probably a VFR. The controller said he was 'sorry'.I assume this plane was on a VFR flight plan at 17;500. I also assume he did get a TCAS alert since he was a jet. We were instructed to descend via TCAS RA because we were initially below him and I assume he was told to climb. But it's my assumption that he didn't want to go into class A airspace so he descended too. This caused our TCAS RA to switch to a climb. This was very dangerous.
Fractional jet Captain reported that they had a near miss during climb.