Broadcasting multiple messages in hypercubes

We investigate T_m(Q_d), the time required to broadcast m⩾1 messages in a d-dimensional hypercube under the telephone model. We give exact values for T_m(Q_d) for m⩽2^d-1 and for m⩾2^d+1. For 2^d-1 +1⩽m⩽2^d, we produce an upper bound which is 1 larger than the lower bound. One consequence of our results is to disprove a lower bound due to Farley (1980)