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I'm sorry but I don't understand your question.  I think you have to provide us more information.

I understand that you don't have to pay any car taxes if you are eligible for a car with #8 plates. Do you have to have cash in the the restricted bank account (equivalent to the tax amount) while you have a #8-plate car? Or is it similar to #7 (diplomatic) plates, where you just buy a car tax-free and don't have to post any cash?

You mean the "yellow" license plates?  Not every car is eligible for tax free purchases.  As I understand it the car has to have been originally brought into Amman on a tax free scheme and can then only be sold to other expats who are eligible for tax free vehicles.  I know my firm, as a non operating foreign office (or however they say it), is only eligible for 1 tax free vehicle.  Although we can ask for an additional one if needed.

Many thanks, thegecko.