  In topological fixed point theory, the Reidemeister trace is an invariant
associated to a selfmap of a polyhedron which combines information from the
Lefschetz and Nielsen numbers. In this paper we define the Reidemeister trace
in the context of $n$-valued selfmaps of compact polyhedra. We prove several
properties of the Reidemeister trace which generalize properties from the
single-valued theory, and prove an averaging formula.
