  A constraint correlation dynamics up to 4-point Green 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 fermion 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 as a quantum expectation value
identically for all times. The same holds for the Ward identities as generated
by commutators of Gauss operators. The constraint dynamical equations are
highly non-perturbative and thus applicable also in the strong coupling regime,
as e.g. low-energy QCD problems.
