At the upper echelon of the thoroughbred breeding business, rich men buy fabulously expensive mares, pay astonishing stud fees and dream about winning classics like the Belmont Stakes.

At the opposite end of the business, occupied for years by the Boniface family of Bel Air, Md., people worry more about survival, about making the mortgage payments on the farm and paying the feed bill for their horses. They may occasionally dream the grand dreams to which all owners are entitled, but any realist knows that rags-to-riches stories don't often happen in this game.

Raising even one horse with the kind of pedigree usually associated with Belmont Stakes winners is even beyond the means of ordinary millionaires. Slew O'Gold, the probable favorite in Saturday's race, was the result of mating a mare worth at least $1 million with a stallion whose stud fee is now $250,000. Even lesser Belmont entrants, like High Honors and Dixieland Band, have bloodlines that are just as expensive.

So the Bonifaces are surely amazed to find themselves in this rarefied atmosphere. But because of their own perseverance, a few strokes of good fortune and the uncommon talent of their colt Deputed Testamony, they could, on Saturday, win the prize most coveted by American breeders.

Bill Boniface Sr. was the racing editor of the Baltimore Sun and his son Billy was serving in the Marines in 1963 when they bought a few acres of what would become Bonita Farm. The tract of land wasn't much, but Billy had a vision: he wanted to run a multifaceted thoroughbred operation and train his racehorses on the farm. While he was overseas, he visited farms in Newmarket, England, where horses were trained by galloping them over the heaths, and he wrote his father an enthusiastic letter, saying, "That's the way to do it." When he was back in the United States, he would come home on the weekends, enlisting the help of Marine buddies, and work on the fences for the farm.

Their early years weren't easy ones. "Sometimes," Boniface Sr. said, "we had to borrow money from the bank to pay the feed bill." And when they bought adjoining pieces of land to enlarge the farm, their resources were sometimes stretched near the breaking point.

The Bonifaces' breeding operation was necessarily modest; people operating at this level of the game must usually deal with other people's castoffs. Bonita Farm got lucky with such a castoff when the blueblood Ogden Phipps stable sold them a colt named Bold Monarch who had shown great promise before breaking down.

He proved to be a very successful stallion, putting the the whole operation on a firmer footing. And Billy proved to be a successful trainer, breaking down many potential clients' prejudices against the practice of training horses on a farm.

But it was a phone call five years ago that would most dramatically alter the Bonifaces' lives. John Williams, the manager of Spendthrift Farm, called Billy and said he had a stallion named Traffic Cop who might do well in Maryland. "Down here," Williams said, "he's lost in the shuffle."

There are two factors that can make a stallion successful. One, of course, is his own genetic makeup, the capacity to pass along running ability to his offpsring. The other factor is what people in the business call "support." If breeders don't send decent mares to a stallion--and especially if they don't send any mares at all--he can't succeed.

There was nothing embarrassing about Traffic Cop's credentials. He was a son of the outstanding racehorse Traffic Judge, and Traffic Cop himself had won stakes at Hialeah and Belmont. But in Kentucky, where the most elite thoroughbred stallions in the world reside, Traffic Cop commanded no interest. In his last season there, he was bred to only seven mares.

"He was the type of horse who would go in Maryland," Boniface Sr. said, and so members of the family got on the phone, selling 20 shares in the stallion to breeders in the state, retaining 20 themselves. They offered his services at stud for a $1,000 fee.

Traffic Cop was proving to be a respectable minor-league stallion at the time he was bred with Proof Requested, who had decent bloodlines but whose performance on the track had been undistinguished. The product of that mating was Deputed Testamony.

Last season, as a 2-year-old, he showed considerable promise. Three weeeks ago, he rallied on the rail to score a stunning upset in the Preakness. Now, he is one of the three strong contenders in the Belmont field. If he wins Saturday, he will make the pedigree experts reflect further on the inexactitude of their science and give hope to every small-time horse breeder who has ever entertained a grand dream.