  The dynamics of a close binary system of globular clusters is considered. It
is shown that the star transfer process from one of the components to the other
should lead to the decrease of dimension of the first cluster with simultaneous
increase of the dimension of the second cluster. The rates of variations of
clusters' sizes due to the mutual tidal interaction between the components, as
well as of the orbital rotation of the binary system on the evolution of
clusters' sizes, are estimated. The results may be attributed to the double
nuclei observed in certain galaxies.
