The power of the brand has been so thoroughly examined in recent years that it is pretty much taken for granted: brands have meaning, brands inspire trust and (crucially) brands command a premium from consumers. Millions of dollars in marketing have chased this idea. How, then, to explain Ol' Roy?

Ol' Roy Dog Food is a ''private label'' product -- what used to be called a ''generic.'' It's a dry dog food made especially for Wal-Mart, which is the only place you can buy it, and its attributes have been extolled in not a single clever TV commercial. Ol' Roy also happens to be the top-selling dog food in America by an annual margin of at least 20 percent, according to Wal-Mart. (Presumably, the closest competitor is Pedigree Dry Food for Dogs, the top name brand by volume with almost 214,000 tons last year, according to Information Resources, a market research company. Wal-Mart does not share its data with such firms.) The story of Ol' Roy, then, is this: in the age of massive and complicated ''brand building'' efforts, a nonbrand is quietly thriving.

When Ol' Roy first appeared in 1981, the idea of the store brand still called to mind plain white packaging with black letters (DOG FOOD) and low quality. Mr. Sam, as Wal-Mart officials still somewhat creepily call the retail giant's deceased founder, Sam Walton, apparently believed that the dry-dog-food market had an empty space at the ''opening price point'' -- that is, the cheap end of the scale. So he asked the Doane Pet Care Company to create a dog food to fill it. The idea was to make something of equal quality to the brand names, but with no marketing costs, and thus to undersell the competition. Roy was the name of Mr. Sam's English setter.

It was, of course, a long road to Ol' Roy's move to the head of the dry-dog-food pack. One key factor, obviously, is that during those 20-some years Wal-Mart became a monstrous force in retailing, with more than 3,000 outlets in the United States and net sales of $245 billion, making it the highest-revenue company in the world. It is now the nation's top seller of groceries, toys and jewelry, among other things. So being sold ''only'' at Wal-Mart is hardly a drawback.