This study involved 72 volunteers divided into two groups according to the apnea-hypopnea index (AHI): AHI>15 episodes per hour (ep/h) (main group, n=39, including 28 men, median AHI 44.15, median age 47), 0≤AHI≤15ep/h (control group, n=33, including 12 men, median AHI 2, median age 28). Each participant underwent polysomnography with a recording of 19 EEG channels. Based on wavelet bicoherence (WB), the magnitude of connectivity between all pairs of EEG channels in six bands was estimated: Df1 0.25;1, Df2 1;4, Df3 4;8, Df4 8;12, Df5 12;20, Df6 20;30 Hz. In all six bands considered, we noted a significant decrease in symmetrical interhemispheric connections in OSA patients. Also, in the main group for slow oscillatory activity Df1 and Df2, we observe a decrease in connection values in the EEG channels associated with the central interhemispheric sulcus. In addition, patients with AHI>15 show an increase in intrahemispheric connectivity, in particular, forming a left hemisphere high-degree synchronization node (connections PzT3, PzF3, PzFp1) in the Df2 band. When considering high-frequency EEG oscillations, connectivity in OSA patients again shows a significant increase within the cerebral hemispheres. The revealed differences in functional connectivity in patients with different levels of AHI are quite stable, remaining when averaging the full nocturnal EEG recording, including both the entire sleep duration and night awakenings. The increase in the number of hypoxia episodes correlates with the violation of the symmetry of interhemispheric functional connections. Maximum absolute values of correlation between the apnea-hypopnea index, AHI, and the WB synchronization strength are observed for the Df2 band in symmetrical EEG channels C3C4 (-0.81) and P3P4 (-0.77). The conducted studies demonstrate the possibility of developing diagnostic systems for obstructive sleep apnea syndrome without using signals from the cardiovascular system and respiratory activity.