Many neuro-degenerative diseases are difficult to diagnose in their early stages. For example, early diagnosis of Mild Cognitive Impairment (MCI) requires a wide variety of tests to distinguish MCI symptoms and normal consequences of aging. In this article, we use the wavelet-skeleton approach to find some characteristic patterns in the electroencephalograms (EEGs) of healthy adult patients and patients with cognitive dysfunctions. We analyze the EEG activity recorded during natural sleep of 11 elderly patients aged between 60 and 75, six of whom have mild cognitive impairment, and apply a nonlinear analysis method based on continuous wavelet transformskeletons. Our studies show that a comprehensive analysis of EEG signals of the entire sleep state allows us to identify a significant decrease in the average duration of oscillatory patterns in the frequency band [12; 14] Hz in the presence of mild cognitive impairment. Thus, the changes in this frequency range can be interpreted as related to the activity in the motor cortex, as a candidate for developing the criteria for early objective MCI.