Abstract: An air dehumidifying apparatus having a cyclone separator, a primary filter, a secondary filter, and a separation membrane element made of a special high polymer for passing steam smoothly and hardly passing air. The elements of the apparatus are disposed in a flow direction of air, so that the air may pass sequentially. Also, a casing is provided for forming an outer wall of the cyclone separator and accommodating the primary and secondary filter and separation membrane element. Large particles of oil, moisture, dust and other foreign matter are removed by the cyclone separator. As a result, the life of the primary filter is extended. By putting the filters and separation membrane element into one casing, the apparatus is reduced in size, and is installed easily.