Deterministic dynamics on stationary point process in Rd are built upon compatible point-shifts: translation invariant mappings from each point of the process to another. When a point-shift is applied multiple times to a point-process it creates a sequence of distributions, namely, the distributions of point process given there is a point of the nth iteration of the point-shift at the origin. We will introduce the notion of marked stochastic point-shifts. Marked Stochastic point-shifts use not only the realization of the point-process to decide how to map each point of the process, but also extra information coming from enlarging the probability space through marks. We will aim for self-contained talk in which examples are provided and the discussion is motivated by an application in the field of theoretical Computer Science.