Text (MM+errata): Enchant creature. ; When enchanted creature is put into a graveyard, return that card to the battlefield under your control. [Oracle 2009/07/08]
Since False Demise's effect follows the standard timing rules for triggered abilities, if both players have False Demise on the same creature, then the player whose turn it is when the creature goes to the graveyard will not get it. The other False Demise effect will fail since the creature will no longer be in the graveyard. [D'Angelo 1999/08/01]
Token creatures are removed from the game prior to False Demise's triggered ability resolving. [Duelist Magazine #12, Page 32] The continuous effect of removing tokens is "faster" than triggered abilities.
