In a recording apparatus (camcorders, optical disc recorders, etc.), the operator presses down priority designating buttons for designating priorities when recording input image data. An additional information generating section records and holds, in a storage section, additional information indicating priorities of data to be recorded (e.g., “low”, “intermediate”, “high”, or “highest”) which are set, depending on what priority designating button has been pressed down. If recordable remaining space in the storage section detected by the remaining amount detecting section falls below a predetermined value before the start of or during recording of data, a control section overwrites regions in order of priority of data which is stored therein, the lowest first, with data which is about to be recorded or is being recorded, based on the additional information generated by the additional information generating section. Therefore, even if free space in the storage medium becomes small, a decisive moment can be recoded, for example.