Delay management is an important issue in the daily operations of any railway company. The task is to update the planned timetable to a disposition timetable in such a way that the inconvenience for the passengers is as small as possible. The two main decisions that have to be made in this respect are the wait-depart decisions to decide which connections should be maintained in case of delays and the priority decisions that determine the order in which trains are allowed to pass a specific piece of track. They later are necessary in the capacitated case due to the limited capacity of the track system and are crucial to ensure that the headways between different trains are respected and that single-track traffic is routed correctly. While the wait-depart decisions have been intensively studied in literature (e.g. [Sch06,Gat07]), the priority decisions in the capacitated case have been neglected so far in delay management optimization models. In the current paper, we add the priority dec...