Hi Marinos,
I just spoke with the Customs and Excise Department last night. There is good and bad news. The good news is that if you are making Cyprus your permanent home and you can prove your absence for a certain amountof years, you are entitled to import one car PER DRIVER in your family free of duty, excise and VAT.
The bad news is that these requirements are reasonably stringent:
1) You need to have had the car for at least 6 Months and USED it during that time
2) The car should have at least 60,000 Kilometres on it
3) You need proof of insurance and registration for 6 months
4) There is a good bit of paperwork and forms to fill out in addition to a number of trips you might have to make back and forth to the import authority
5) There is the possibility of being rejected for exception by an official that simply wants to charge you. They did not tell me this but if you look on the site:
http://www.mof.gov.cy under Customs and Excise you will find the documentation you need and it seems clear that it is not a foregon conclusion that no tax will be charged.
I was all ready to import a car but we've not owned it for 6 months and would need to show insurance for it. It is a shame. Let me put it this way. I have an ML320. To import it with excise would come to around USD50,000. I am not sure what other people here have been quoting in terms of rates, but this is directly from the Department in Cyprus.
Best to you!