A connecting piece for a duct such as a ventilation duct is provided and includes an inner flow space in communication with the interior of the duct, the connecting piece having at least one joining portion on which an end region of the duct is slidable and fixable. The connecting piece includes a compressed fiber material and a binder. The connecting piece displays a substantially configurationally stable portion in association with the joining portion, and the connecting piece displays, at least interiorly, a layer which is impervious to a fluid, in particular a gas, this layer being adjacent the inner flow space of the connecting piece.