1. An electronic monetary system comprising: an issuing bank having a first on-line accounting system; electronic representations of money that are credited in said first on-line accounting system as current liabilities of said issuing bank; a money generator module that generates said electronic representations of money; a first teller module, associated with said issuing bank, that stores said electronic representations of money; a plurality of correspondent banks, each having a second on-line accounting system and each maintaining an account at said issuing bank; a plurality of second teller modules, each associated with one of said correspondent banks, that each store said electronic representations of money; a transaction module that stores said electronic representations of money, performs on-line transactions with said plurality of correspondent banks, and exchanges said electronic representations of money with other transaction modules in off-line transactions; where said first teller module has a first processor that intermediates transactions among said first on-line accounting system, said money generator module, and said second teller module; and where said second teller module has a second processor that intermediates transactions among said second on-line accounting system, said first teller module, and said transaction module.