<p><b>Abstract</b>—We present an algorithm for the gossiping problem defined over an <tmath>$n$</tmath> processor communication network, <tmath>$N$</tmath>, where message multicasting is allowed. The algorithm generates a communication schedule with a total communication time at most <tmath>n + r</tmath>, where <tmath>r</tmath> is the radius of the network. Our algorithm begins by constructing a spanning tree (or tree network <tmath>T</tmath>) with the least possible radius. Then, all the communications are carried out in the tree network as follows: Each processor waits its turn to transmit "almost" consecutively to its parent and children all the messages in its subtree. During other times, each processor transmits to its children all the messages emanating elsewhere in the network.</p>