A multiple window display system includes a display device and a screen ownership area pointing to the identity of the window which is to contribute the data for each display area of the display device. An ordered list is maintained of the active windows in the priority order thereof. Means are provided to regenerate the screen ownership area from the ordered list, on each change made to the list, in terms of list position per device display area, by overwriting, progressing through the list in order of increasingly significantly priority order, the list indicating, in each position thereof, the identity of the window having the respective priority. The list contains the addresses of the windows in storage and the type thereof. The screen ownership area is reset to the lowest potential priority list position value and is overwritten.