Abstract: Process for the exhaust dyeing of wound bodies of synthetic or natural fiber materials with appropriate dyestuffs, by heating the wound-up textile articles to temperatures ranging at or above 100.degree. C while replacing the air in the dyeing vessel by saturated or superheated steam, and by preparing the dye bath in the batch vessel which is connected by pipes with the dyeing vessel, and heating up the dyebath to temperatures also ranging at or above 100.degree. C. A special control of the temperature and of the steam pressure in both closed systems is provided to secure the formation of a relative excess pressure of 2.94 to 9.8 bars in the batch vessel or such an excess pressure is produced from the outside. The hot dyebath is pressed by the differential pressure over a period of 3 to 60 seconds at the same time from inside and outside into the dry or wet wound bodies.