Culture vessels for cell cultures having at least one cell culture chamber containing a cell culture mixture that is separated by a dialysis membrane from a nutrient medium in a nutrient supply chamber. Nutrients are transported through the dialysis membrane into the cell culture chamber and metabolic products are transported out of the cell culture chamber into the nutrient supply chamber. To provide a culture vessel for generating cell cultures with a high cell density that is economical to manufacture and easy to handle and to reduce the danger of infections, a gas exchange membrane, that at least partly delimits the cell culture chamber and that is impermeable to liquids and to microorganisms that could contaminate the cell cultures is provided for feeding the gases required for cell culturing to the culture chamber and for discharging the gases generated during cell culturing.