This paper presents a mathematical mechanism for neuronal synchronization in oscillatory brain activities on the basis of the layer structures with recurrent inhibition. To begin with, a linear theory reveals that the recurrent inhibition tends to cause a synchronous uniform oscillation if the loop delay increases, and that an oscillating neuron recruits neighboring neurons by delivering synchronous inputs through the recurrent inhibition loop if the frequency is that of the selfexcitatory oscillation. Then, a quasilinearized dual wave model (DWM), employing the two-sinusoids plus bias input describing functions (TSBDF), shows the competitive relationship between the synchronous oscillation and a spatial wave that is introduced to represent normal brain activity patterns. Results of computer simulations conform well to the predictions of the DWM. Thus, synchronous brain activities are suggested to be the result of the spatio-temporal filter characteristics of the brain layer structures, modified by the neural nonlinearity.