A theory for studying the properties of N-component disorder materials is developed. It takes into account the short-range correlation effect of nearest-neighbor atoms and includes various disorder arrangements of atoms from segregation to forming N-component compound within the same framework. The method to calculate the density of electronic states of disorder materials using extended Cluster-Bethe-Lattice Green function with a tight-binding Hamiltonian is present in detail. As an application, we calculated the densities of states of ternary disorder alloys AxByCz(x + y + z) =1 under various concentrations and different correlation parameters. The results show strikingly the effects of correlation among the atoms and of disorder on the densities of states.