An air-supply device for supplying breathing air into a breathing-air region. An inflow opening connected to an outflow region via an interior. An outflow region connected to the outflow region via the interior. The outflow region formed on a flexible, air-permeable material. For flexible use of the air-supply device and to avoid significant adverse effect to a user, provision is made for the air-supply device to have a sheet-like, flexible portion, which has a first flat side and a second flat side, located opposite the first. The outflow region arranged on the first flat side. The interior formed between the first flat side and the second flat side. In the interior, at least the outflow region has arranged on it at least one spacer, which prevents the outflow region from butting against the second flat side.