A system for cleaning the air, such as air in the interior of motor vehicles, airplanes, buildings or shelters, having organic substances such as alcohols, alkanes and aliphatic and aromatic hydrocarbons. The air cleaning system includes a cylindrical adsorber. The cylindrical adsorber has a plurality of circular segments for passing air to be cleaned and for passing desorption air through the adsorber. The adsorber contains adsorption agents, such as a hydrophobic zeolite, that can be regenerated with microwaves. The air cleaning system also includes a microwave unit disposed on adsorber and an oxidation catalyst.