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This really isn't specific to amex (and amex does offer conventional limit cards) - but the no preset limit doesn't mean you can spend as much as you want. In essen there is a limit, you just don't know about it. Once you reach that internally kept limit the charges may be approved, or may be not. In case of amex for instnace if you're trying to buy more than they are comfortable with they'll likely give you a call and ask for some financial info.