An analysis of the simple movement bimanual reaction among 10 groups of students of different age (7-17 years old) allowed to find out significant reduction of delays of movement responses with the progress of age. This was also accompanied by a trend to the reduction of asimmetry of time of right and left-hand reactions. Both indices had fluctuating variables, very complicatedly interrelated, and changing synchronically until the age of 11-12, and in different directions after it. The study of the obtained data from the view of contemporary ideas about the functional interspheric brain asimmetry as well as about fluctuating processes in psychophysiological functions leads to an assumption that the age of 11-12 years is a critical period in the development of movement asimmetry in man.