A pipe device includes a pipe and a connection element. The pipe has a pipe jacket that has an inner surface and an outer surface and forms a flow channel. The connection element forms a through-channel that extends from a connection piece consisting of a first material (M1) and having a first opening to a second opening. The pipe jacket is positioned on the connection piece with a first pipe end consisting of a second material (M2). A bonded connection is formed between the first material (M1) and the second material (M2) in a contact region between the inner surface of the pipe jacket and a peripheral surface of the connection piece.