A friend from my cinquecento car club is doing it and I went to last years rally start at Hyde Park as well as doing some research myself for maybe a shot at 2007.
Diesel is scarce over there as well as good quality petrol. Also you’ve got to remember the environment you’ll be travelling in and so it's favourable to have a car many people in that region know and will know how to fix/have parts for because you WILL break down
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Also you should need to think of fitting new suspension to any car you get as it will take a hammering over the Mongol ruts (most of the fragile 2CV’s and Morris Minors that made it to Mongolia literally broke in half within a country from the finish).
You want an eastern European tub such as a cinquecento, 126, Trabant, Lada or any other commie box from the 80’s – mid 90’s. A Japanese Kei car just won’t hack it I’m afraid.
Also forget about a return journey unless you want to be gone 6 weeks so don’t get a nice car. One team last year set out in a brand new looking MK2 bubble micra which they left in Mongolia though they did make it.
If you want to gamble for Japanese reliability in exchange for not being able to have parts to fix it in a scrape, get an older car like a MK1 micra or a small engined 4×4 like a Suzuki SJ.
Pleeease don’t take another classic Panda 4×4 to it’s grave as they are getting rare but take a bog standard one by any means but they are Italian built so harder to fix when you’re in somewhere like darkest Russia with a vodka swilling mechanic.
Other tips are take as much fuel and spares as you can carry, thermal protection as it gets cold on Mongolian nights and sleeping in the car is likely as well as plenty of foreign money/vodka to bribe the police as they will stop you in Russia for no reason frequently.
If you want nutty, maybe try a Daihatsu Hi-jet campervan but you’re screwed if it breaks down and needs a specific part.
Could also try a Reliant Robin. It’s been tried every year but nobody has yet made it through France; go against the odds
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A co-driver and basic specific car mechanical knowledge is also vital. I’m sure you know half this but you gotta realise the degree of a challenge this will be.