Earlier this year, a single share in Seattle Slew changed hands for $3 million. With 40 shares in the syndicate that controls him, the transaction indicates that the stallion is worth about $120 million. He is, by far, the most valuable horse in history.

This figure may seem outlandish, but a glance at the two major races being run Saturday will suggest why Slew is so extraordinary. His son, Slew o' Gold, will be an odds-on favorite to win the rich Jockey Club Gold Cup at Belmont Park and complete a sweep of New York's fall championship series. Another of his offspring, Seattle Song, will be a prime contender in the Washington, D.C. International after establishing himself as a top racehorse in France.

The achievements of these horses, in addition to Swale, Landaluce, Slewpy and others, have made Seattle Slew a phenomenon in the breeding world. "In terms of figures and averages," said Bill Oppenheim, whose newsletter Racing Update compiles many of those figures, "Seattle Slew has made the best start at stud of any horse ever."

Slew, of course, was a great racehorse who possessed brilliant speed and the stamina to win at 1 1/2 miles. He certainly was eligible to become a great stallion, although there is no logical reason why, of the Triple Crown winners of the 1970s, he has been so brilliant while Secretariat was unspectacular and Affirmed was an out-and-out failure. That's one of the mysteries of genetics.

But the record is unambiguous. In his first two crops of horses -- the ones who are 3-year-olds and 4-year-olds this season -- Slew has had eight Grade I stakes winners. And what is so impressive about them is the diversity of their achievements.

Even the greatest of sires tend to beget a certain type of horse who will do some things brilliantly and others less well. Sons and daughters of Northern Dancer excel in long-distance European grass racing; you wouldn't want them running six furlongs on the dirt in the United States. Bold Ruler was the greatest sire before Northern Dancer, but his scions tended to run out of gas when they went 1 1/4 miles or farther.

But Seattle Slew's offspring seemingly can do anything. His colts in Saturday's stakes races support that contention. Slew o' Gold always possessed high speed, but as he matured he showed that his real forte is stamina; 1 1/2 miles is probably his most effective distance. He won the Jockey Club Gold Cup last year, and he will be an overwhelming favorite to do it again Saturday. Not only does he have talent, he has a measure of character. He has been winning this fall with a foot injury that has hindered his effectiveness, but he still has beaten every challenger.

Whereas Slew o' Gold was a late bloomer, Seattle Song was highly precocious. In the second start of his career, he won a seven-furlong stakes race in France, and this year he has run well against top competition at 1 1/4 miles. By proving that Seattle Slew offspring can handle the grass, he stimulated great European interest in the sire at this summer's yearling sales.

The only knock against Seattle Slew is that his offspring tend to be either stars or nonentities, with little in between. More than half his foals have never won a race. But the prospect of getting another Slew o' Gold or Swale or Seattle Song has driven the price for his genes to amazing heights. His yearlings cost an average of $1.3 million each this year. One breeder offered to buy a 1985 stud service to Slew for $800,000 -- and was turned down.

"A lot of people are investing in Seattle Slew on the assumption he is the successor to Northern Dancer," Oppenheim said. Inasmuch as Northern Dancer is the most prolific sire of stakes winners in history, and his blood will influence the development of the species for generations to come, that's a mighty big assumption. But all that Seattle Slew has done so far has suggested that he can, indeed, be a sire of such stature.