For instance, customers can log on and access any of the 22 account services the bank offers, from its brokerage to its mortgage lending division.

A few local customers logged on for some hurried moments to check for e-mail.

With an encrypted password, customers can log on to the Internet almost anywhere in the city, according to Azulstar's chief financial officer, Les Lewis.

By early April, Ms. Grant said, more than 2,500 potential customers from 27 countries had logged onto the systems to try them.

If the customer has logged in to E*Trade's site, the representative can even see what page that person is on.

When customers log in from the computer they used to enroll, they are shown the chosen image and phrase for verification.

When customers log on to the appropriate Web site, Mr. White and his colleagues take the initiative.

In December its customers logged a record 102 million hours on line, up from 45 million hours in September.

But persuading some customers to log on in the first place is difficult.

When paying a utility or other company directly, customers can log on to its Web site and authorize a credit card or debit payment.