It is pointed out that experimental work has shown that for the transpiration of moisture through hygroscopic materials two distinct regions of relative humidity can be distinguished: (i) A region below some value between 70 and 80% where the moisture movement is proportional to the vapour pressure difference, and (ii) a region of high relative humidity where the moisture movement is not directly proportional to the vapour pressure. A theory is advanced that these two regions correspond to the two conditions in which water may be present in a hygroscopic material: (i) the water may be molecularly adsorbed, that is to say, the water is bound by the affinity of the molecules of water for those of the solid on which it is adsorbed; (ii) the water may be held in small fissures in the sub-microscopic structure of the sorbing material by capillary forces. The mechanism by which the moisture will move through the material would be different in the two cases and would result in the distinction between regions of high and of low relative humidity. A short discussion is given of Fick's law showing the form in which it might be expected to apply in the two cases. Measurements are given for fibreboards showing that below 75% relative humidity the resistance of the board to moisture transpiration is proportional to the thickness. The moisture content gradients through fibreboard samples have been determined. The diffusance through a board in which the moisture content gradient is opposed to the vapour pressure gradient shows that the latter is the important factor, and the determination of the moisture content gradient indicates that at these low humidities Fick's law is applicable.