Methods of operating facsimile machines are provided in which a priority table is stored that specifies printing priorities for different types of designated information. A message along with associated image data and first designated information and other messages having other associated image data and other designated information are received. The first designated information and other designated information are then detected. Printing of the associated image data is then controlled based on relative priority of the first designated information with respect to other designated information that have been detected. In one possible implementation, facsimile machines are provided that can include, for example, a receiving unit and control unit. When a first printing job is being executed that includes image data to be printed, the receiving unit receives a communication message having second printing job associated therewith. The second printing job includes other image data. The communication message includes designated information indicating that the second printing job is higher in a printing priority order than printing of the image data associated with the first printing job. The control unit interrupts execution of the first printing job, and executes the second printing job.