Here is some useful info for vehicles from a local site.
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CROSSING AZERBAIJAN WITH YOUR OWN VEHICLE
There are 2 ways to cross Azerbaijan territory with your own vehicle. It is either to transit Azerbaijan or apply for temporary entry (up to 30 days).
Temporary entry (up to 30 days)
At the link below you can find regulations on foreign registered vehicles entry to Azerbaijan.
http://www.customs.gov.az/ru/pravtamofo.html
Unfortunately that information is in Russian, we will quote below just some extras in English which we believe might be helpful to independent travellers.
3. ŠŃŠµŠ¼ŠµŠ½Š½ŃŠ¹ ввоз ŃŃŠ°Š½ŃпоŃŃŠ½ŃŃ
ŃŃŠµŠ“ŃŃŠ² на ŃŠ°Š¼Š¾Š¶ŠµŠ½Š½ŃŃ ŃŠµŃŃŠøŃŠ¾ŃŠøŃ ŠŠ·ŠµŃŠ±Š°Š¹Š“Š¶Š°Š½ŃŠŗŠ¾Š¹ Š ŠµŃŠæŃблики ŃŠøŠ·ŠøŃŠµŃŠŗŠøŠ¼Šø Š»ŠøŃŠ°Š¼Šø
3. Temporary entry of transport vehicles to the territory of Azerbaijan by individual persons.
3.1. Š¢ŃŠ°Š½ŃпоŃŃŠ½Ńе ŃŃŠµŠ“ŃŃŠ²Š° Š²ŃŠµŃ
виГов, взŃŃŃŠµ на поŃŃŠ¾ŃŠ½Š½ŃŠ¹ ŃŃŠµŃ в иноŃŃŃŠ°Š½Š½ŃŃ
гоŃŃŠ“аŃŃŃŠ²Š°Ń
, Š“ŠµŠŗŠ»Š°ŃŠøŃŃŃŃŃŃ ŃŠøŠ·ŠøŃŠµŃŠŗŠøŠ¼Šø Š»ŠøŃŠ°Š¼Šø в ŃŠ°Š¼Š¾Š¶ŠµŠ½Š½Š¾Š¼ Š¾ŃŠ³Š°Š½Šµ, ГейŃŃŠ²ŃŃŃŠµŠ¼ в ŠæŠ¾Š³ŃŠ°Š½ŠøŃном ŠæŃопŃŃŠŗŠ½Š¾Š¼ ŠæŃŠ½ŠŗŃе, в Š¾ŃноŃении ниŃ
оŃŃŃŠµŃŃŠ²Š»ŃеŃŃŃ ŃŠ°Š¼Š¾Š¶ŠµŠ½Š½Ńй конŃŃŠ¾Š»Ń, Ń Š»ŠøŃŠ°, ŠæŠµŃŠµŠ¼ŠµŃаŃŃŠµŠ³Š¾ ŃŃŠ°Š½ŃпоŃŃŠ½Š¾Šµ ŃŃŠµŠ“ŃŃŠ²Š¾, Š±ŠµŃŠµŃŃŃ Š¾Š±ŃŠ·Š°ŃелŃŃŃŠ²Š¾ об Š¾Š±ŃаŃном Š²Ńвозе ŃŃŠ°Š½ŃпоŃŃŠ½Š¾Š³Š¾ ŃŃŠµŠ“ŃŃŠ²Š° Šø Š²ŃŠ“аеŃŃŃ ŃŠ°Š·ŃŠµŃŠµŠ½ŠøŠµ на его Š²ŃеменнŃй ввоз на ŃŠ°Š¼Š¾Š¶ŠµŠ½Š½ŃŃ ŃŠµŃŃŠøŃŠ¾ŃŠøŃ ŠŠ·ŠµŃŠ±Š°Š¹Š“Š¶Š°Š½ŃŠŗŠ¾Š¹ Š ŠµŃŠæŃблики.
3.1. Transport vehicle of any type registered in other country have to be declared by individual person at Customs station operating at border point. Obligation to leave with vehicle Azerbaijan is taken from individual and permission is given for temporary entry to Azerbaijan territory.
3.2. Š ŃŠ»ŃŃŠ°Šµ ŠµŃŠ»Šø ŃŃŠ°Š½ŃпоŃŃŠ½Ńе ŃŃŠµŠ“ŃŃŠ²Š°, Š²ŃŠµŠ¼ŠµŠ½Š½Š¾ Š²Š²Š¾Š·ŠøŠ¼ŃŠµ в ŠŠ·ŠµŃŠ±Š°Š¹Š“Š¶Š°Š½ŃŠŗŃŃ Š ŠµŃŠæŃŠ±Š»ŠøŠŗŃ Š½Š° ŃŃŠ¾Šŗ Го 30 (ŃŃŠøŠ“ŃŠ°ŃŠø) Гней Šø Š¾ŃŠ½Š¾ŃŃŃŠøŠµŃŃ Šŗ ŃŠ¾Š²Š°Ńной гŃŃŠæŠæŠµ 8703 Š¢Š ŠŠŠ, ввозŃŃŃŃ Š½ŠµŠæŠ¾ŃŃŠµŠ“ŃŃŠ²ŠµŠ½Š½Š¾ ŃŠøŠ·ŠøŃŠµŃŠŗŠøŠ¼Šø Š»ŠøŃŠ°Š¼Šø-Š½ŠµŃŠµŠ·ŠøŠ“ŠµŠ½ŃŠ°Š¼Šø, ŃŃŠ°Š½ŃпоŃŃŠ½Š¾Šµ ŃŃŠµŠ“ŃŃŠ²Š¾ Š¾ŃŠ¾ŃŠ¼Š»ŃŠµŃŃŃ ŃŠ°Š¼Š¾Š¶ŠµŠ½Š½Ńм Š¾Ńганом, ГейŃŃŠ²ŃŃŃŠøŠ¼ в ŠæŠ¾Š³ŃŠ°Š½ŠøŃном ŠæŃопŃŃŠŗŠ½Š¾Š¼ ŠæŃŠ½ŠŗŃе, без Š²Š½ŠµŃŠµŠ½ŠøŃ ГенежнŃŃ
ŃŃŠµŠ“ŃŃŠ² на Š“ŠµŠæŠ¾Š·ŠøŃŠ½Ńй ŃŃŠµŃ Šø ŠæŃŠøŠ½ŃŃŠøŠµŠ¼ Š¾Ń Š»ŠøŃŠ°, ŠæŠµŃŠµŠ¼ŠµŃаŃŃŠµŠ³Š¾ ŃŃŠ°Š½ŃпоŃŃŠ½Š¾Šµ ŃŃŠµŠ“ŃŃŠ²Š¾, Š¾Š±ŃŠ·Š°ŃелŃŃŃŠ²Š° об Š¾Š±ŃаŃном Š²Ńвозе ŃŃŠ°Š½ŃпоŃŃŠ½Š¾Š³Š¾ ŃŃŠµŠ“ŃŃŠ²Š°.
3.2. If transport vehicle entering Azerbaijan territory for a period of up to 30 days is listed in '8703 Š¢Š ŠŠŠ' and is taken by an individual person who is non-resident of Azerbaijan then official documents are issued by Customs station operating at border point without taking money deposit and but just obligation that vehicle will leave Azerbaijan territory within 30 day period.
Here is link to LP Forum with comments of the driver that crissed AZ in his own vehicle:
Travelling to Azerbaijan with a Foreign Car - My Experience - Lonely Planet travel forum
Entering Azerbaijan through the Lagodekhi- Belakan border crossing (Mazim Ćay):
I got a 30 days permit for the car. I had to pay 15USD road tax and 5USD (actually it is 2,5AZN but they charge 5USD) for an insurance (third party liability of course). You must pay in USD. The insurance covered up to 1000AZN of property damage and up to 5000AZN of body harm. Azerbaijan was the only country of the Caucasus which had an (compulsory)insurance available at the border. I also had a secondary cover third party liability insurance with Ingosur (up to 1.000.000USD).
Azeri law allows you to enter for up to 30days without leaving a deposit(don't do this, because there is no bank to get your money back at the border) with a foreign-registered car IF:
Your car is owned by yourself. (no leasing).
It is a car (not a motorbike).
It is a left-hand drive (no hand-drive cars are allowed in the country (like most UK cars)). (Which, BTW is illegal because it violates the provisions of the Vienna/Geneva Road Traffic Conventions, of which Azerbaijan is a signatory country).
It has normal registration plates (no transit ones).
All this is written on the web site of the Azeri customs (in Azeri and Russian only, of course

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They were very friendly on the border crossing. It took about 2 hours both sides. There were 3 more cars. I got about 6 or 7 different and very beautiful papers on the Azeri part.
Source: LP Forum, qwer1234
Transit
Transit is allowed for 72 hours only. Customs declaration and obligation to leave with vehicle the territory of Azerbaijan will be taken from you. Unless you leave a full-value cash deposit back at the border (which will be returned to you when you exit), you may only keep the car in for 72 hours since you enter Azerbaijan. $15 road tax have to be paid. Otherwise, for periods exceeding 72 hours a several thousands deposit for the car has to be paid, and you must use the same entry and exit points to get the deposit back. For example, for the motorbike the deposit is around $3500 USD. They don't accept credit cards obviously.
We can also recommend you to check Forum
Azerbaijan - Lonely Planet travel forum where you can find some useful information.
Read a post here.
Right hand drive vehicles in Azerbaijan
Right hand drive vehicles are illegal in Azerbaijan and officially are not allowed to enter. Official Regulations (only in Russian) are available here:
http://www.customs.gov.az/ru/pravtamofo.html
8.1. ŠŠ²Š¾Š· в ŠŠ·ŠµŃŠ±Š°Š¹Š“Š¶Š°Š½ŃŠŗŃŃ Š ŠµŃŠæŃŠ±Š»ŠøŠŗŃ ŃŃŠ°Š½ŃпоŃŃŠ½ŃŃ
ŃŃŠµŠ“ŃŃŠ² Ń ŃŃŠ»ŠµŠ¼ на ŠæŃавой ŃŃŠ¾Ńоне Š·Š°ŠæŃеŃаеŃŃŃ.
8.1. RHD vehicles are not allowed to enter the territory of Azerbaijan Republic.
Transit is not an option for RHD, which are not even allowed to enter Azerbaijan territory according to regulations.
Despite the fact that officially RHD vehicles are banned in Azerbaijan most (if not all) tourists manage to cross Azerbaijan without any hassle.
At the link below you can learn about experience of other people non-residents of Azerbaijan who tried to cross Azeri territory with RHD vehicles.
Right hand drive vehicles in Azerbaijan. - Lonely Planet travel forum
Azerbaijan with a RHD car - Lonely Planet travel forum
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Hope this info is useful
Samy