INSTRUCTOR WITH INST STUDENT WERE IN A HOLDING PATTERN WHEN THEY NOTICED A 'VELOCITY' ACFT ON A COLLISION COURSE. THEY TOOK EVASIVE ACTION WITH DIVE AND TURN ONLY TO HAVE THE SECOND ACFT MIMIC THEIR ACTIONS AND REMAIN IN CLOSE PROX.

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MY STUDENT AND I WERE HOLDING OVER THE VRB VOR ON AN IFR CLRNC AT 4000 FT. WE HAD BEGUN OUR INBOUND TURN ON THE 300 DEG RADIAL WHEN I NOTICED A VELOCITY ACFT AT OUR ALT TURNING TOWARD US FROM THE NE AT OUR ALT. I THEN TOOK THE CTLS; AND WHEN I REALIZED A NEAR COLLISION WAS IMMINENT; I DOVE SHARPLY TO THE L AND LOST ABOUT 1800 FT. THE VELOCITY ACFT FOR ONE REASON OR THE OTHER FOLLOWED US DOWN FROM 4000 FT FLYING NEARLY 100-200 FT OFF OUR R WING. MY STUDENT COULD SEE THE PLT'S FACE. I THEN CONTINUED TO TURN AWAY FROM THE OTHER ACFT AND PROCEEDED TO CONTACT ZMA TO TELL THEM WHAT HAPPENED AND WHY I HAD DEVIATED IN ALT. THE OTHER ACFT THEN FLEW AWAY FROM US TO THE W. MIAMI INFORMED US A PREVIOUS ACFT HAD RPTED SUSPICIOUS ACTIVITY FROM THE SAME ACFT IN WHICH WE WERE INVOLVED WITH; BUT THEY COULD NOT PICK HIM UP ON RADAR BECAUSE HE EITHER HAD NO XPONDER OR DID NOT HAVE IT ON. MIAMI COULD ONLY GET A FAINT PRIMARY TARGET. I DO NOT KNOW WHAT PROMPTED THIS OTHER PLT'S ACTIONS. I DO NOT SEE ANY OTHER WAY THAT I COULD HAVE AVOIDED THIS ACFT EXCEPT BY DIVING SHARPLY DOWN AND TO THE L.