Among plenty of agencies, Eurosynapses, in my opinion, is one of the best.
They are really very experienced and qualified. Their cooperation with the MOH of Saudi Arabia is very strong and with with many Private hospitals as well. I had no misunderstanding working with Eurosynapses. An interview was right in time, all details were explained correctly. Even now they keep on holding connection.
If you want to try yourself in Middle East, I would strongly recommend to contact them first!