Try doing a search for NJME or NAS and the answer to your question can be found in the Middle East forum.
The bones of it are that NAS operate two BBJs from Riyadh on behalf of the Saudi Ministry of Finance, whereas NJME operate various corporate jets from Jeddah. There is also the A319CJ operation which operates a scheduled service within the region, again based in Jeddah (I think).
As I said, there is lots of info in the ME forum and not much of it is favourable.
Hope this helps.