Flexible covalent-organic frameworks (COFs) display a variety of guest-dependent dynamic behaviors, but because these are an emerging class of materials, very little experimental adsorption data exists. This work examines the adsorption properties of COF-506 and COF-506-Cu utilizing various adsorbates as probe molecules. These materials have small surface areas (<100 m2/g) but still have significant capacity for methanol and isopropanol compared to activated carbon, even though the COF contains approximately 1/10th the surface area of many activated carbons. Isotherms for ethane/ethylene collected up to 1 bar show moderate selectivity for ethylene, but interestingly, this selectivity is reversed when the isotherms are measured up to 5 bar. The change in selectivity occurs because the ethane isotherm has a distinct stepwise increase in capacity near 4 bar. The adsorption data indicate broad generalizations and analogies of COFs to activated carbon should be avoided; that the adsorption capacity COFs may not correlate to surface area; and that high-pressure adsorption isotherms may have steps in the adsorption isotherm where capacity increases significantly.