  This paper establishes that the strong converse holds for some classes of
discrete memoryless multimessage multicast networks (DM-MMNs) whose
corresponding cut-set bounds are tight, i.e., coincide with the set of
achievable rate tuples. The strong converse for these classes of DM-MMNs
implies that all sequences of codes with rate tuples belonging to the exterior
of the cut-set bound have average error probabilities that necessarily tend to
one (and are not simply bounded away from zero). Examples in the classes of
DM-MMNs include wireless erasure networks, DM-MMNs consisting of independent
discrete memoryless channels (DMCs) as well as single-destination DM-MMNs
consisting of independent DMCs with destination feedback. Our elementary proof
technique leverages properties of the R\'enyi divergence.
