An analog Hopfield neural network with excitatory and inhibitory connections and three time delays was studied. The neural networks demonstrated synchronous outputs shortly after the initial conditions. The networks with excitatory connections demonstrated either output decay or output growth until saturation at the constant value. The networks with inhibitory connections showed either decaying oscillations or growing oscillations until saturation of their amplitudes. An increase of the time delay in one, two, or three inhibitory subnetworks resulted in various activities, such as the smooth amplitude and period growth, multiresonances of amplitudes, oscillation period jumps, and period-tripling bifurcations. In several cases of subnetwork configurations, oscillation periods demonstrated discrete ranges of changes, similar to the discrete oscillation rhythms in the human and animal electroencephalogram.