The invention provides an Internet banking system which can present services more familiar to daily life of individual users, and a bank server apparatus, etc. which can limit available banking services depending on user attributes. From the viewpoint of security, the invention reduces risks of information leak from a client terminal device to third persons and unauthorized accesses from third persons. Banking software for connection to the bank server apparatus is installed in the client terminal device. The banking software can display a screen transfer, etc. in the off-line condition. The banking software prepares transaction instruction data from information entered by the user on the displayed screen and temporarily holds it in the client terminal device. When the client terminal device is connected to the bank server apparatus, the held data is uploaded to the bank server apparatus. In the client terminal device, application software can be utilized in linkage with the banking software so as to display the contents of an electronic bankbook. As examples of the application software, household account-book software, petty cashbook software, etc. can be provided to users.