A model able to describe the effect of structural changes in the adsorbent or adsorbed phase during the dynamic (breakthrough) separation of mixtures on metal-organic frameworks (MOFs) is presented. The methodology is exemplified for a few pertinent case studies: the separation of xylene isomers and ethylbenzene on the flexible MOF MIL-53 and the rigid MOF MIL-47. At low pressures, no preferential adsorption of any component occurs on both MOFs. Contrarily, at higher pressures separation of ethylbenzene (EB) from o-xylene (oX) occurs on MIL-53 as a result of the breathing phenomenon within the MIL-53 structure. The increase in selectivity, starting from the gate-opening pressure, could be modeled by using a pressure-dependent saturation capacity for the most strongly adsorbed component oX. In the separation of m-xylene (mX) from p-xylene (pX) on the rigid MOF MIL-47, separation at higher pressures is a result of preferential stacking of pX. Here, the selectivity increases once the adsorption of pX switches from a single to a double file adsorption. By implementing a loading dependent adsorption constant for pX, the different unconventional breakthrough profiles and the observed selectivity profile on MIL-47 can be simulated. A similar methodology was used for the separation of EB from pX on MIL-47, where the separation is a result from steric constraints imposed onto the adsorption of EB.