Curiosity about the activity of neural networks in the human brain results from the search for definition of human self-consciousness as an identifier of human personality. Today, the RS-fMRI technology occupies a leading position among methods used to study this problem. The widespread use of the technology is limited by certain drawbacks. Starting from 2010, there is a growing interest in the possibility of using neurophysiological methods for the diagnosis of the brain's default mode network (DMN) state based on the analysis of EEG microstates. The study was aimed to demonstrate the possibility of recording the activity of brain networks both at rest and under exposure to the stimulus evoking a known response. A total of 42 people underwent assessment in the relaxed wakefulness state with the eyes closed that involved extraction of certain EEG microstate sequences and the EEG inverse problem solution. The data obtained were tested for adequacy via comparison with the results obtained by the preset stimulation of auditory and language function. The conclusion was made about the possibility of assesing the brain's DMN’s activity by combining the analysis of EEG microstates with the EEG inverse problem solution. The proposed technology can be used in both scientific research and clinical practice in the form of new techniques and systems allowing one to determine alterations in neuropsychological processes.