We present a mean field model for a spiking neural network of excitatory and inhibitory neurons with fast GABA \(_{{\textbf {A}}}\) and nonlinear slow GABA \(_{{\textbf {B}}}\) inhibitory conductance-based synapses. This mean field model can predict the spontaneous and evoked response of the network to external stimulation in asynchronous irregular regimes. The model displays theta oscillations for sufficiently strong GABA \(_{{\textbf {B}}}\) conductance. Optogenetic activation of interneurons and an increase of GABA \(_{{\textbf {B}}}\) conductance caused opposite effects on the emergence of gamma oscillations in the model. In agreement with direct numerical simulations of neural networks and experimental data, the mean field model predicts that an increase of GABA \(_{{\textbf {B}}}\) conductance reduces gamma oscillations. Furthermore, the slow dynamics of GABA \(_{{\textbf {B}}}\) synapses regulates the appearance and duration of transient gamma oscillations, namely gamma bursts, in the mean field model. Finally, we show that nonlinear GABA \(_{{\textbf {B}}}\) synapses play a major role to stabilize the network from the emergence of epileptic seizures.
