To ensure during the braiding of braiding cores, which have a complex braiding core geometry or vastly different side lengths, that the braiding threads are always correctly following the braiding core contour in terms of storage, at least two braiding rings are provided, which have a constant opening cross-section and are arranged in series directly adjacent to one another. The opening cross-sections delimited by the braiding rings overlap at least partially. The braiding rings are adjustable independently of one another.