The Al-MOF CAU-13 ([Al(OH)(trans-CDC)]; trans-H2CDC = trans-1,4-cyclohexanedicarboxylic acid) is structurally related to the MIL-53 compounds that are well-known for their "breathing" behavior, i.e., the framework flexibility upon external stimuli such as the presence of adsorbate molecules. The adsorption properties of CAU-13 were investigated in detail. The sorption isotherms of N2, H2, CH4, CO, CO2, and water were recorded, and the adsorption enthalpies for the gases were determined by microcalorimetry. The structural changes upon adsorption of CO2 were followed with in situ synchrotron powder X-ray diffraction (PXRD). The patterns were analyzed by parametric unit cell refinement, and the preferential arrangement of the CO2 molecules was modeled by density functional theory calculations. The adsorption and separation of mixtures of o-, m-, and p-xylene from mesitylene showed a preferred adsorption of o-xylene. The structures of o/m/p-xylene-loaded CAU-13 were determined from PXRD data. The adsorption of xylene isomers induces a larger pore opening than that in the thermal activation of CAU-13. In the crystal structure of the activated sample CAU-13(empty pore), half of the linkers adopt the a,a confirmation and the other half the e,e conformation, and the presence of a,a-CDC(2-) ions hampers the structural flexibility of CAU-13. However, after the adsorption of xylene, all linkers are present in the e,e conformation, allowing for a wider pore opening by this new type of "breathing".