Abstract: To print air-permeable textile material (8), successive areas (5) of the textile material (8) to be printed are brought incrementally into an area (5) covered by at least one ink jet print head (1). By means of the ink jet print head (1) ink is selectively applied to the textile, according to predetermined picture information. Ink applied to the textile material (8) is finally subjected to a treatment for fixing the ink. By keeping the textile material (8) tensioned in the area (5) covered by the ink jet print head (1) over a free space (28) on the side of the textile material (8) remote from the ink jet print head (1), an improved penetration and adhesion of the ink and a limitation of the spreading of the ink are ensured. Furthermore, an apparatus for printing textile tensioned over a free space is described.