Player enjoyment is perhaps the most important issue in successful game design, but is previously not addressed in the area of Pervasive games. Departing from the GameFlow model of player enjoyment in computer gaming, this paper presents an initial outline for a new model of Pervasive player enjoyment- the Pervasive GameFlow model. The suggested model is described and discussed in terms of additions and elaborations in relation to the GameFlow model, and is intended to serve as a departing point for further empirical studies of player enjoyment in Pervasive games.