To substantiate a term "asymmetry of consciousness", to throw light on it are compared disturbances of consciousness in dextral and sinistral persons with selective lesions in the right or left brain hemispheres. Is supposed a fundamental role of the spatial-temporal factors. By them are mediated relations "brain-consciousness", asymmetry of consciousness. The latter is expressed in dextral persons by an opposite spatial-temporal organization of psycho-sensory (which are realized in individual present and past) and psychomotor (which are displayed in external present and future) processes. This contrast is not observed in sinistrals or only in some of them. Is assumed a probability of evolution of space and time with appearance of their forms having been absent before the human level. They are presumably described by the authors as individual space and time, on the one hand being determined by the functioning brain of each dextral and sinistral person, on the other hand defining the limits and limitations of the mental abilities of each person. Individual space and time may be other in a sinistral person than in a dextral one.