Let G be a finite group written additively and S a non-empty subset of G. We say that S is e-exhaustive if G=S+...+S (e times).
The minimal integer e >0, if it exists, such that S is e-exhaustive, is called the
exhaustion number of the set S and is denoted by e(S). The exhaustion numbers of various subsets of finite abelian groups have been determined by the author <1>. In this paper the exhaustion numbers of maximal
sum-free sets of the cyclic groups of prime power order are determined.