Try these:
http://www.expatjob.net/Obviously navigate your way to Middle East - many vacancies are advertised via agencies but some are direct hire from companies........so you will have to build you own database.
Be warned however (or maybe not if you are looking for a job) if you subscribe you will be emailed daily (and I mean every day 7 days per week) with new positions for you to sift through.
It started out as an "Engineering" site for the likes of me many years ago but has expanded into teaching, medical, accounting, IT etc etc globally.
I will reitterate, many positions are advertised via agencies but there are direct hire appointments there too containing some if not all the details you want.
Hope it helps
