The paper presents a polynomial-time algorithm for rescheduling traffic when one track of a double-track railway becomes unavailable, the remaining track has a siding, and there are two categories of trains—priority trains such as passenger trains and ordinary trains such as the majority of freight trains. The presented algorithm minimises the negative effect, caused by the track blockage, first for the priority trains and then for the ordinary trains on the set of all schedules optimal for the priority trains.