Data of literature about morphological, functional and biochemical specificity of the brain interhemispheric asymmetry of healthy right-handers and left-handers and about peculiarity of dynamics of cerebral pathology in patients with different individual asymmetry profiles are presented at the present article. Results of our investigation by using coherence parameters of electroencephalogram (EEG) in healthy right-handers and left-handers in state of rest, during functional tests and sleeping and in patients with different forms of the brain organic damage were analyzed too. EEG coherence analysis revealed the reciprocal changing of alpha-beta and theta-delta spectral bands in right-handers whilein left-handers synchronous changing of all EEG spectral bands were observed. Data about regional-frequent specificity of EEG coherence, peculiarity of EEG asymmetry in right-handers and left-handers, aslo about specificity of EEG spectral band genesis and point of view about a role of the brain regulator systems in forming of interhemispheric asymmetry in different functional states allowed to propose the conception about principle of interhermispheric brain asymmetry formation in left-handers and left-handers. Following this conception in dextrals elements of concurrent (summary-reciprocal) cooperation are predominant at the character of interhemispheric and cortical-subcortical interaction while in sinistrals a principle of concordance (supplementary) is preferable. These peculiarities the brain organization determine, from the first side, the quicker revovery of functions damaged after cranio-cerebral trauma in left-handers in comparison right-handers and from the other side - they determine the forming of the more expressed pathology in the remote terms after exposure the low dose of radiation.