  A constraint correlation dynamics up to 4-point Green's functions is proposed
for SU(N) gauge theories which reduces the N-body quantum field problem to the
two-body level. The resulting set of nonlinear coupled equations fulfills all
conservation laws including baryon number, linear and angular momenta as well
as the total energy. Apart from the conservation laws in the space-time degrees
of freedom the Gauss law is conserved identically for all times. The constraint
dynamical equations are highly non-perturbative and thus applicable also in the
strong coupling regime as e.g., low-energy QCD problems.
