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This paper considers the issue of broadcasting protocols in multihop radio networks. The objective of a broadcasting protocol is to deliver the broadcasted message to all network nodes. To efficiently achieve this objective the broad- casting protocol in this paper utilizes two basic properties of the multihop radio network. One is the broadcast nature of the radio which allows every single trasmission to reach all nodes that are in line of sight and within range of the transmitting node. The other, spatial reuse of the radio channel, which due to the multihop nature of the network allows multiple simultaneous transmissions to be received correctly. The proposed protocol incorporates these properties to obtain a collision free forwarding of the broadcasted message on a tree. Centralized and distributed algorithms for the tree construction are presented. The obtained trees are unique in incorporating radio oriented time ordering as part of their definition. In this way multiple copies of one or more broadcasted messages can be transmitted simultaneously without collision, requiring only a small number of message transmissions. Consequently, the protocol not only guarantees that the broadcasted message reaches all network nodes in bounded time, but also ensures that the broadcasting activity will use only limited channel bandwidth and node memory. The proposed broadcast protocol thus possesses the advantages of TDM solutions while allowing the channel bandwidth to be shared, concurrently with the broadcast, with other transmission activities as dictated, for instance, by data link protocols. Some NP-completeness proofs are also given.