In this study, the cross-sections of the 129Xe(n,n‘)129mXe and 131Xe(n,n’)131mXe reactions were measured for the first time within the energy range 13.5–15.0 MeV based on the 27Al(n,α)24Na monitor reaction cross-section. The experiment employed high-purity, high-pressure, and highly enriched 129,131Xe isotope gas as the target sample. This study marks the first instance in which the measured cross-sections, corresponding correlation matrices, and associated uncertainties are provided. The TALYS-1.96 software was employed to obtain theoretical calculations, allowing for a comparison with experimental and evaluation results. The present study aids in understanding 129Xe(n,n‘)129mXe and 131Xe(n,n’)131mXe cross-sections within 14 MeV regions, where the energy dependence exhibits relatively gradual changes and significant discrepancies between nuclear data libraries have been identified.