The minimum phase property of single-input single-output linear compartmental systems (i.e. networks of linear reservoirs) is considered in this paper. The analysis shows that minimum phase cannot be lost through cascade and feedback connections and that acyclic networks of reservoirs are minimum phase provided all the reservoirs have roughly the same time constant and all the paths from input to output go through almost the same number of reservoirs. The conjunctive use of these results often allows one to ascertain the minimum phase of a complex compartmental system. Some extensions to larger classes of dynamical systems are discussed at the end of the paper.