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We present a model of (double) kinetic theory which paves the way to describe matterin a Double Field Theory background. Generalized diffeomorphisms acting on doublephase space tensors are introduced. The generalized covariant derivative is replaced bya generalized Liouville operator as it happens in relativistic kinetic theory. The sectioncondition is consistently extended and the closure of the generalized transformations is stillgiven by the C-bracket. In this context we propose a generalized Boltzmann equation andcompute the moments of the latter, obtaining an expression for the generalized energymomentum tensor and its conservation law.