Abstract: An on-line (Internet or web-based) auction intended for selling real property and other unique items has several features and advantages adopted for such transactions. In one version, a descending price auction is used with the price descending at time intervals in unpredictable increments; the first bidder acquires the property. An unpublished reserve price is set initially by the seller, but he can lower the reserve price during the auction if desired. Typically the seller pays the auction organizer an up-front fee which is a percentage of the property's listing price before the auction. The buyer also pays a percentage of the purchase price to the auction organizer when the property is sold. In another type of auction, the price is incremented at amounts determined by the auction organizer, and amongst several bidders at each successive price level, only one is randomly chosen, the randomly chosen bidder is sold the property when there are no bidders at the next higher price level.