I found the following helpful hints in "buying a car on Ebay" on the Edmunds.com website. It was written by Jim Kneiszel.

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Also see my companion guide on the topic of  Quick Guide to Selling Your Car.
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eBay car buying tips:

Narrow the search: Choose a make and model, then hit eBay. It's easier to make frequent checks on the auction market by using an exact model in the eBay search field.

Don't get an itchy finger: Watch the auctions for a while before bidding. Hit the "watch this item" feature to track sales and search "completed items" to track final sale prices.

Use the eBay buyer tools: Be sure to check the feedback from other buyers regarding the seller. Make sure the individual is rated as a seller, not a buyer. Read the auction description carefully and request more photos by e-mail if necessary.

Call the seller: It can be reassuring to develop a rapport with the seller, and sale terms may be more flexible than you think.

Look for no-reserve auctions: Find the seller who doesn't set a minimum winning bid amount, which often is as high as the car's retail value.

Make sure you have an out: Bid only on auctions where sellers allow you to cancel after you inspect the car.

Cash is king: While the banking industry is getting more creative about financing online purchases, most interstate transactions are cash sales.

Have the car inspected by a mechanic: Contact a mechanic in the city where the car is being sold and arrange for an inspection when you arrive. The eBay site offers inspection services in 50 major metro markets, as well as a free limited warranty for the drive home for many cars.

Use Carfax: The company's $24.99 online vehicle history report can tell you where the car has been, its accurate mileage and whether it has been damaged in a crash or flood.

Use on-line pricing services: Free services like the True Market Value system at Edmunds.com give a quick, realistic idea on retail and wholesale values of used cars.

Bid and walk away: Decide on a fair price for a car, then bid and walk away. Don't get caught up in a bidding war and end up paying too much.

Factor in travel or delivery costs: Remember you have to pick up the vehicle or have it shipped when you win the auction. Include gas, hotels, food, lost work time and plane tickets in the cost.

Buy round-trip plane tickets: A discount round-trip fare is often cheaper than a one-way ticket, and it gives you flexibility if you decide you don't want the car when you see it.