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In this study, we consider the problem of signal processing in neuron–astrocyte networks where the intercellular communication is described on the basis of a tripartite synapse concept. This type of communication involves combined contributions of pre- and postsynaptic neuronal compartments and components of the surrounding astrocyte to the processes of information transmission. Astrocyte-mediated regulation of neuronal activity is considered through the analysis of the response changes in the classical Hodgkin–Huxley model driven by excitatory synaptic current. It is shown that the complicated astrocyte-dependent dynamics of this current can lead to non-trivial changes in individual postsynaptic neuronal activity and, hence, in the cooperative activation of neuronal groups linked by the “astrocyte-mediated bridge”.