We introduce the problem of a single source attempting to communicate information simultaneously to several receivers. The intent is to model the situation of a broadcaster with multiple receivers or a lecturer with many listeners. Thus several different channels with a common input a lphabet are specified. W e shall determine the families of simultaneously achievable transmission rates for many extreme classes of channels. Upper and lower bounds on the capacity region will be found, and it will be shown that the family of theoretically achievable rates dominates the family of rates achievable by previously known timesharing and maximin procedures. This improvement is gained by superimposing high-rate information on low-rate information. All of these results lead to a new approach to the compound channels problem.