  The dynamics governing the evolution of a many body system is constrained by
a nonabelian local symmetry. We obtain a general form of the global macroscopic
conditions assuring that at the microscopic level the evolution respects the
overall symmetry constraint. These conditions does not depend on detailed
dynamics of the system. It is shown that a nonabelian internal symmetry leads
to the new subsidiary condition imposed on the system. A structure of
constraints is analysed.
