In this talk we investigate the quantum Einstein-Yang-Mills sector quantised by the methods of Loop Quantum Gravity (LQG). We derive a Hamiltonian describing the Yang-Mills interaction including the gravitational quantum field and compare it to pure quantum Yang-Mills theory on a fixed, classical background spacetime as was considered by Kogut and Susskind. Furthermore, we develop a calculational scheme by which the fundamental spectrum of the quantum Yang-Mills Hamiltonian can be computed in principle.