Gossiping of a single source with multiple messages (by splitting information into pieces) has been treated only for complete graphs, shown to considerably reduce the completion time, that is, the first time at which all network nodes are informed, compared with single-message gossiping. In this paper, gossiping of a single source with multiple messages is treated, for networks modeled as certain structured graphs, wherein upper bounds of the high-probability completion time are established through a novel “dependency graph” technique. The results shed useful insights into the behavior of multiple-message gossiping and can be useful for data dissemination in sensor networks, multihopping content distribution, and file downloading in peer-to-peer networks.