The method of moments is used to derive exact analytical solutions for an open priority queueing system with preemption-distance priorities and feedback. Customers enter from outside in a Poisson stream. They can feed back for several times, changing priorities and service demands in an arbitrary manner. During feedback they can fork and branch according to user-defined probabilities. The service demands of the different classes are pairwise independent and can be arbitrarily distributed. A customer who has been interrupted resumes his service from the point where he was interrupted (preemptive resume). A system of linear equations is to be solved to obtain the mean sojourn times of each customer class in the system.