First of all, you must know what death means.
According with the above definition (courtesy of St. Gregory Palamas), you will see that there are two deaths.
Perhaps we must stress here, before answering, that both Angels and Demons in your text are ...Angels, because Devil is not a definition of species but a definition of behavior.
Because angels (good and bad) are incorporeal they are not subject of the first death.
So, since devils are good by nature but evil in intention, they are the only ones from the angels which suffer the second death.
Bonus point #1: Any intelligent entity (angel, human soul) is eternal by God's grace. It will not cease to exist.
Bonus point #2: Humans are the only ones which are subjects to the first death (all of us) and, possibly, subjects of the second death (God forbid!).