  We generalize three main concepts of Gabor analysis for lattices to the
setting of model sets: Fundamental Identity of Gabor Analysis, Janssen's
representation of the frame operator and Wexler-Raz biorthogonality relations.
Utilizing the connection between model sets and almost periodic functions, as
well as Poisson's summations formula for model sets we develop a form of a
bracket product that plays a central role in our approach. Furthermore, we show
that, if a Gabor system for a model set admits a dual which is of Gabor type,
then the density of the model set has to be greater than one.
