We show that the identification (ID) capacity of the two-receivers broadcast channel is the set of rate pairs satisfying that, for some distribution on the input, each receiver's ID rate does not exceed the mutual information between the input and the output that it observes. The capacity's interior is achieved by codes with deterministic encoders. Our results hold under the average error criterion, which requires that each receiver reliably identify its message if the other receiver's message is uniformly distributed. Key in the proof is a new ID code for the single-user channel.