A B757 HAS A TCAS RA DUE TO CONFLICTING B737 IN ZJX CLASS A AIRSPACE.

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ZJX ISSUED HOLDING PATTERN E OF ORM AT FL350. I HAD JUST ENTERED HOLDING WHEN TCASII RA OCCURRED. TCASII AURAL WARNING TO CLB. TFC 10 O'CLOCK POS AT FL350. I VISUALLY ACQUIRED THE TFC AS I BEGAN A CLB TO AVOID THE B737 WHICH WAS ALSO TAKING EVASIVE ACTION. INFORMED ZJX THAT I WAS RESPONDING TO TCASII RA. ATC INSTRUCTED TO DSND TO FL330. I SUSPECT THAT ZJX HAD BOTH ACFT AT FL350 AND WAS UNAWARE OF THE CONFLICT. TCASII WORKED GREAT. ZJX WAS VERY BUSY AT THE TIME OF THE EVENT UNKNOWN ACFT IN ZMA'S AIRSPACE. THE PROBABILITY OF THIS KIND OF EVENT OBVIOUSLY INCREASES WHEN UNKNOWN ACFT ENTER CLASS A AIRSPACE AND ATC IS FORCED TO PUT OTHER ACFT IN HOLDING IN ORDER TO SORT OUT THE UNKNOWN TFC IN THEIR AIRSPACE. I ASKED ZJX WHAT HAD INITIATED THE HOLDING REQUIREMENT AND HE RESPONDED 'ALL I KNOW IS THAT I HAVE TFC IN MY SECTOR AND WE DON'T KNOW WHO THEY ARE.' THIS SEEMS TO IMPLY THAT THE SUSPECT ACFT CREW NEEDS TO BE TRAINED IN PROPER IFR/ATC PROCS BEFORE BEING ALLOWED TO OPERATE AGAIN IN CTLED AIRSPACE.