A method of event-related potential (ERP) investigation for brain research is proposed that is based on analysis of the structures of chains of local maxima that are obtained using the matrix of square coefficients of the wavelet transform of ERP. The general approach to ERP analysis by this method is presented, which ensures the formation and separation of the chains of local maxima and minima in the matrix of square coefficients of the ERP wavelet transform. Algorithms for the adaptive recovery of ERP elements after for- ward wavelet transform are described, which are based on the time scaling of wavelet transform coefficients that reflects separate elements of ERP components. In using the proposed method for the analysis of the visual ERP, it is established out that ERP components consist of no less than two to three elements representing particular regions in the time and frequency domains. These regions provide a basis for the adaptive recovery of ERP elements having certain latent time and amplitude characteristics, which can be of special clinical and physiological significance. The proposed method is stable with respect to a change in the wavelet function (Morlet, WAVE) used for the ERP analysis. Application of this method to studying the steady-state visual evoked potential (SSVEP) induced by photostimulation revealed, in addition to the main element corresponding to the visual stimulus frequency, new elements that are not always recognized in the conventional SSVEP spectrum. © Pleiades Publishing, Inc., 2015.