Kay Kennemer, 58, knew exactly where to turn for information after a recent doctor's visit by her elderly mother: the medical sites on the World Wide Web.

"I was interested in something the doctor said to my mother," remembered Kennemer, who also uses the Internet to send e-mail across Texas and New Mexico to her family and friends. "And I thought, `Let me just go check this out."'Once the domain of the young and technically inclined, the Internet increasingly is taking root with a wide cross section of Americans.

A new study estimates that more than a third of adult Americans now use the Internet, an increase of more than 18 million - or 34 percent - in just nine months. Among the fastest-growing groups online were blacks and Indians, as well as young adults 16-24 and women over 50.

The study showed an increase of 50 percent in the number of American women over 50 using the Internet during the nine months ending in June, accounting for nearly 5 million users. The numbers of men under 50 using the Internet grew almost half as fast during the same period.

"It is absolutely mind-boggling - I think everything in the world is there," said Kennemer of Austin, Texas. She recently graduated from high-tech classes offered by Green Thumb Inc., a nonprofit group that offers computer training for seniors.

The study released Tuesday by Nielsen Media Research and CommerceNet estimated that 70.2 million Americans over 16 use the Internet. That represents 35 percent of adult Americans; the same study in September 1997 counted 52 million adult Americans online, or 26 percent.

And for the first time, the report said, the majority of Americans between 16-24 are using the Internet - about 18.8 million of them, including 70 percent of men in that age group and 51 percent of women.

"I'm still pretty new to it," confessed Diane Park, a social worker near Seattle and an Internet neophyte who logs on from her local library. She owns an older computer and can't afford to buy a new one powerful enough to use the Internet. "It takes time figuring out all the different search engines. I don't know quite all that's out there."

Tuesday's study estimated 40.1 million American men and 30.1 million women use the Internet, and that the percentage growth among men and women overall during the nine-month period was about the same.

But a closer look at the figures showed the largest gains in Internet use among Asians and blacks.

The Nielsen-CommerceNet study was based in part on random telephone interviews with 4,042 people in the United States during June 1998. The September study was based in part on telephone interviews with 7,157 Americans.

People who had used any part of the Internet - e-mail, the Web, FTP, telnet, chat rooms or discussion groups - during the past month were counted as Internet users.

No margin of error was noted, but surveys with much smaller samplings, typically 1,000 or so people, generally have a margin or error of about 3 percentage points.

A summary of the report is available on the Web at (www.commerce.net/research). The full report costs $5,000.