Another 16.28 million investors could begin trading on-line in two to three years, according to an on-line survey of 20,119 people.

If that migration occurs, the value of assets held in on-line accounts could increase by more than $1.1 trillion, according to the survey, which was conducted by the electronic commerce consulting firm Gomez Advisors Inc. of Lincoln, Mass., and Harris Interactive, a Rochester, N.Y.-based market research company.

About three million off-line investors plan to open an on-line brokerage account within six months, the survey suggests. And the 12.77 million off-line investors who use the Internet for research are seen as likely candidates for on-line trading. Some 5.1 million investors have traded on-line at least once during the past six months.

Most of these potential investors are a different breed from those already trading on-line, said Alex Stein, a co-founder of Gomez Advisors.

Most Internet investors are day traders and "serious" investors, Mr. Stein said. However, most of the new on-line traders are likely to be long-term investors or one-stop shoppers seeking a single site from which to conduct both banking and investment activities.

One-stop shoppers constitute only 5% of on-line investors, he said, though 25% of all investors who trade on the Web have on-line bank accounts.

Mr. Stein said the number of survey respondents who reported trading through bank-owned brokerages was negligible, but the findings could bode well for banks with on-line brokerage capabilities.

"This shows there's a ready market for bank brokerages, and the market's barely been tapped," he said.

But brokerages, bank-owned or not, must improve their service and image to appeal to the next wave of investors.

"The new wave requires more advice, a higher service level, and interactivity with their broker," he said. On-line brokers must overcome lingering perceptions that they are less accountable to their customers than traditional brokers, he added.

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