The lack of reliable information on the absorption of moisture by hygroscopic textiles at high humidities has hitherto prevented the resolution of certain anomalies. In the present paper the conditions for the attainment of atmospheres of high humidity are discussed and new techniques are shown to be necessary. The main requirements are conditions favouring rapid transfer of moisture to the sample and adequate temperature control. A simple new apparatus is described together with the experimental methods employed. The results given show much higher sorption at very high humidities than has been previously reported, but there is no true equilibrium at saturation. The immediate saturation regain is, for practical purposes, identical with the moisture held by the fibres after centrifuging wet samples under standard conditions. It is concluded that the hysteresis loop closes at saturation. Other related phenomena are discussed.