The hypothesis of communication through coherence proposes that coherent or synchronous oscillations in connected neural systems can promote communication. It has been applied mainly to how oscillations interact in connected networks. We tested by simulations whether information transmission about an external stimulus from one network to a second network is influenced by gamma oscillations, by whether the oscillations are coherent, and by their phase. Gamma oscillations were induced by increasing the relative conductance of AMPA to NMDA excitatory synapses. It was found that small associative connection strengths between the networks were sufficient to produce information transmission (measured by Shannon mutual information) such that the second attractor network took the correct decision based on the state of the first network. Although gamma oscillations were present in both networks, the synaptic connections sufficient for perfect information transmission about the stimulus presented to the network (100% correct, 1 bit of information) were insufficiently strong to produce coherence, or phase-locking, between the two networks; this only occurred when the synaptic strengths between the networks were increased by > 10 ×. Further, the phase of the oscillations between the networks did not influence the information transmission or its speed at these connection strengths. Moreover, information transmission was as good when the AMPA-to-NMDA ratio was reduced to its normal value, and oscillations were not present. Similar results were found when the second network was not an attractor decision-making network. Thus information transmission can occur before synapses have been made sufficiently strong to produce coherence.