A data-processing system consisting of a portable terminal device and a copying machine can effectively work with protection against breakage of data stored in the terminal device. The data-processing system is constructed to work on the following principle: When a given period is measured by a timer for starting the power saving mode, a portable terminal device provides a copying machine with a signal informing of starting the power-saving mode. The copying machine, which received the power-saving-mode starting signal, provides in later the portable terminal device a signal requiring the terminal to cancel the power-saving-mode. When a given period is measured by a timer for starting the power saving mode, the copying machine provides the portable terminal device with a signal requiring the terminal device to start the power-saving mode. A CPU, which received information on request of power-saving-mode, executes the power saving mode. The portable terminal device and the copying machine as the former being mounted on the latter can simultaneously execute the power saving mode, preliminarily sheltering data in the storage.