Actually, the NYSE does have an auction: perhaps not in the traditional European sense though.
It has an opening auction which works exactly the same as most European Stock market Auctions: limit and market orders allowed. The uncrossing can take a long while.
The closing auction is an order matching process and is over pretty quickly. Orders for the closing have to be placed in the market by 15:40 US time - except on triple witching when they must be placed by 15:30 - and then the Specialist uncrosses at the close. The market is notified of imbalances at 15:40 ish, and the whole process is controlled by the Specialist.
Hope this helps. Customers that I deal for place alot of orders for market at close in the States. Heaven only knows why: personally I think its just an excuse for the Specialists to make another few dollars for doing nothing.