When Microsoft stock was at a record high in 1999, and its market capitalization was nearly $620 billion, the notion that Apple Computer would ever be bigger — let alone twice as big — was laughable. Apple was teetering on bankruptcy. And Microsoft’s operating system was so dominant in personal computers, then the center of the technology universe, that the government deemed the company an unlawful monopoly.

This week, both Microsoft and Apple unveiled their latest earnings, and the once unthinkable became reality: Apple’s market capitalization hit $683 billion, more than double Microsoft’s current value of $338 billion.

At Apple’s earnings conference call on Tuesday, its chief executive, Timothy D. Cook, called the quarter “historic” and the earnings “amazing.” Noting that Apple sold more than 34,000 iPhones every hour, 24 hours a day, during the quarter, he said the sheer volume of sales was “hard to comprehend.”

Apple earned $18 billion in the quarter — more than any company ever in a single quarter — on revenue of $75 billion. Its free cash flow of $30 billion in one quarter was more than double what IBM, another once-dominant tech company, generates in a full year, noted a senior Bernstein analyst, Toni Sacconaghi. The stock jumped more than 5 percent, even as the broader market was down.