A third of Internet users who manage their investments on-line said they most frequently turn to AOL Personal Finance, according to the market research firm Cyber Dialogue. Another 14% go most often to Quicken.com, and 11% to Yahoo!Finance.

No banks made the list, which New York-based Cyber Dialogue compiled from telephone surveys of 1,000 Internet users and 500 nonusers.

"This demonstrates that the power of the 'portal' is enormous and speaks to the trust in the brand that consumers show toward the consolidators," said David Fenichell, vice president of Cyber Dialogue. "But it remains to be seen if this will continue over time."

More than 18 million Internet users regularly tap into the World Wide Web to conduct some form of investment activity, more than double the 7.8 million measured by Cyber Dialogue in the second quarter of 1997. Cyber Dialogue research found that almost seven million Internet users bank on- line, and eight million intended to within the next 12 months.

With the majority of Internet financial consumers going through sites that consolidate a number of services in one place, "banks have to do a better job extending their brands into the on-line space," said Mr. Fenichell.

He recommended that banks enhance their Internet services, eliminate bill-payment fees, and consider the Internet one piece of a coordinated effort to reach consumers. "The way to make on-line banking attractive is to make it part of a bank's overall service offering," he said. "The Internet should be just another channel that customers want."

Others contend banks are well positioned to build an effective on-line presence, even without attracting the numbers of customers going to consolidators' sites.

"The strategy is to build loyalty, not to get the volume of customers that Schwab has," said Paul Fiore, president and chief executive officer of Digital Insight, a Calabasas, Calif.-based provider of Internet software.

"I don't buy that the number of sites will condense to just a few consolidators," Mr. Fiore said. "I'd bet that there will be more rather than fewer financial sites" because of the complex web of loyalties between consumers and financial providers.

Alper Caglayan, vice president, solutions design at Bowne Internet Solutions, a New York-based Internet banking software provider, said the quantity and accuracy of information banks have on their customers can help them sell additional services later.

"One of the problems of the portals is the accuracy of the information provided" by consumers, he said. "Who are you going to trust with your financial information-Amazon.com or BankBoston?"

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