In the last years Anomalous Small-Angle X-ray Scattering became a precisequantitative method resolving scattering contributions two or three orders of magnitudesmaller compared to the overall small-angle scattering, which are related to the so-calledpure-resonant scattering contribution. Additionally to the structural information precisequantitative information about the different chemical constituents of multi-componentsystems like the fraction of the chemical components localized in the nanostructure of thematerials are obtained from these scattering contributions. The application of the Gausselimination algorithm to the vector equation established by ASAXS measurements at three Xrayenergies is demonstrated for three examples from chemistry and solid state physics. Allexamples deal with the quantitative analysis of the Resonant Invariant (RI-analysis). From theintegrals of the pure-resonant scattering contribution the chemical concentrations in nanoscaledphases are determined. In one example the correlated analysis of the ResonantInvariant and the Non-resonant Invariant (NI-analysis) is employed. The structural andquantitative informations are correlated to the macroscopic properties respectively to theproperties of the phase diagrams of the analyzed materials.