  This work focuses on Exchangeable Occupancy Models (EOM) and their relations
with the Uniform Order Statistics Property (UOSP) for point processes in
discrete time. As our main purpose, we show how definitions and results
presented in Shaked, Spizzichino and Suter (2004) can be unified and
generalized in the frame of occupancy models. We first show some general facts
about EOM's. Then we introduce a class of EOM's, called
$\mathcal{M}^{(a)}$-models, and a concept of generalized Uniform Order
Statistics Property in discrete time. For processes with this property, we
prove a general characterization result in terms of $\mathcal{M}^{(a)}$-models.
Our interest is also focused on properties of closure w.r.t. some natural
transformations of EOM's.
