'Follow That Bugatti Royale, Driver - and Step on It!'

It's the perfect automobile out of which to pass a jar of Gray Poupon. This 1931 Bugatti Royale, a 20-foot-long chauffeur-driven car, is known as the Mona Lisa of cars. Its estimated worth: up to $20 million.

Here at the 25th annual Barrett-Jackson Classic Car Auction, all eyes feasted on this gleaming, dark-blue-and-silver classic with its equally long pedigreed name of ''Bugatti Royale Type 41 Binder Coupe de Ville.''

One of only six left in the world, and the sole Bugatti Royale for sale in the high-rolling realm of car collecting, it was the centerpiece of the four-day auction that drew a record crowd of 80,000 last week.

Collectors say the big crowd indicates that a flat market for classic cars has started to turn around. Eight years ago, prices for older American and European classic cars were climbing. But when the economy turned down, prices fell.

''Prices have almost stabilized now,'' says Bill Noon, sales manager for a Ferrari dealer in La Jolla, Calif., ''and people are back into the market.''

Part of the Bugatti's appeal stems from its history as well as its rarity and quality. Cars used in movies, or formerly owned by celebrities, or with unusual technology fetch higher prices.

To save this Bugatti from Hitler's minions in World War II, it was hidden in a Paris sewer. The current owner, retired Air Force Gen. William Lyon of California, has held the car in his private collection since the mid-1980s.

While negotiations at the auction for the Bugatti were private and are continuing, some 800 other restored cars were up for bid. Dusenbergs, Packards, Cadillacs, Ferraris, Auburns, Corvettes, Thunderbirds, Mercedes-Benzes, Jaguars, and dozens of American cars from the 1950s and '60s were driven to the auction block. The Barrett-Jackson auction, one of the biggest in the United States, often sets prices for the rest of the year.

Wealthy collectors and dealers gather here from around the world to be part of a glitzy, noisy crowd reveling in an auto-lover's buffet. Many top-end collectors, who may own dozens of rare cars apiece, come because specific cars are appearing on the market.

Others own three or four cars, or meticulously restore one car at a time and offer it at this or other auctions throughout the United States. There were 1,400 registered bidders here, a record.

''Like a lot of other things in life, it's 'let the buyer beware,' '' says Geary Bush, a former classic-car owner from Sun City, Ariz. ''You really have to know what you are doing at this or any auction.'' Some car restorations are thoroughly documented down to the serial number on a muffler. Others can be less precise or candid about their authenticity.

A bidder here should be able to assess how much diligence and integrity went into a car restoration, and also be aware of the nuances when the bidding moves swiftly.

''It's not always clear if there are real bids in the room,'' says an official of a West Coast auction house who declined to elaborate on the record, ''because the rapid style of auctioning here can be confusing. You're not sure of what is going on. And in a weak market, I think this can affect prices because some people are terrified to raise their hands.''

A few wealthy collectors, like Jerry Moore of Houston, have hundreds of cars in their collections. Mr. Moore, who owns resort hotels and other real estate, has a museum in his home town that holds 700 of the rarest cars in the world.

''After 700 cars, you get a little choosy,'' he says with a smile as he stands next to a 1953 two-tone red Chrysler Ghia with a hemispherical V8 engine. Only three others are known to exist. A final bid of $148,000 brought the car into his collection. He also sold a 1948 Tucker for $236,000 at the auction. ''It drives like a tank,'' he says of the Tucker, an innovative car that featured a middle headlight that turned with the wheel - and a surplus helicopter engine for a power plant.

''I look for rarity,'' he says, ''and is the car real, or redone too much? It's better for me to buy it restored - let the other guy do the work.''

Moore has a preferred status at auctions because of his collection. Here, he stood near the auctioneer, signaling discreetly while bidding on a cream-colored 1935 Auburn 851 Convertible Sedan. Moore stopped bidding at $60,000. ''The car needed too much work,'' he explained later.

Former baseball star Reggie Jackson owns about 50 rare cars, most of them American autos from the 1950s and '60s.

''The classic cars don't do much for me,'' he says at the auction, where five of his cars were up for bid. ''I had a l955 Chevy when I was a kid,'' he says, ''so I like the cars from that era. I used to have 80 cars, but I'm not in this just for the investment. I love these cars.''

Sentiment and love of rare cars often outweigh prices when nonprofessional collectors explain their reasons for buying.

''There are really two kinds of buyers,'' Mr. Noon says. ''Those who buy on emotion, and the established collector who changes his mind often. Then there's the lady who says, 'I went to the prom in a l949 Mercury,' and she goes out and buys a 1949 Mercury.''

Restoration of old cars is usually done by professionals hired by individuals, or the restorers put their own restorations on the market. Chuck Gambill of Hinsdale, Ill., who retired from owning an oil and gas company, took more than 500 photographs of 1948 Jaguars before his 1948 Mark IV Drophead was restored by professionals.

Standing next to the highly polished restored car - a gray-and-dark-green auto with that classic Jaguar look - Mr. Gambill says this is his fourth restoration. ''I call this my 'coffee can car,' because most of it was disassembled in coffee cans when I bought it in Mississippi,'' he says. It took him eight years to restore it ''To me, this is a piece of art I saved from the scrap pile,'' he says.

When Gambill's Jaguar was on the auction block, the high bid was $55,000, not enough to suit him, so it was not sold. ''I'm still talking with some buyers,'' he says from his home after the auction.

Cars are offered either on ''reserve,'' meaning the owner will not sell the car below a base price, or ''no reserve,'' which enables the highest bidder to buy the car. If a reserve car does not sell, many owners place the car on the post-sale lot, where potential buyers gather for further negotiations.

For Phoenix professional golfer Ron Doan, the auction simply was a chance to buy a good used car. ''I wanted a good second car for daily use,'' he says.

When a l965 Chevrolet with only 39,000 miles on it came on the block, Mr. Doan bid $5,200 and got it. ''I thought it would sell for around $9,000,'' he says. ''I'll drive it for three or four years and then sell it. Where else can you get an older American car that is in better shape?''

Frank Burkdoll of Vacaville, Calif., restored a stunning red 1935 Mercedes-Benz 500K Cabriolet with right-hand drive. ''I paid $3,200 for it in l966,'' he says, standing beside the sparkling car parked in a row of cars under a huge white tent. ''If it doesn't bring $500,000 now, I'm taking it home.''

When the car was auctioned later that day, bidding started at $200,000. ''It went up quickly and reached $400,000,'' Mr. Burkdoll says, ''then it sort of hung there.'' Minutes later, without a sale, the auctioneer went on to the next car.

''I'm thinking of taking it to another auction,'' Burkdoll says from his home. ''For me, the fun went out of driving it after it was restored. I really can't afford it now.''

Some of the top-selling cars at the auction: a 1930 Bentley Speed Six Corsica for $1.1 million; a 1961 Ferrari GT SWB California Spyder for $800,000; a l953 Cadillac Eldorado Convertible for $135,000; and a 1958 Chevrolet Impala Convertible for $51,000.