Apparatus for erection of a tower of several levels, arranged one above the other, whereby an assembly is attachable at the top of the tower, comprising the following components: a) a structure being placeable at the top of the tower under erection and made of frames with several frame sections, which has a clear height and a clear width which are selected as large that the free space spanned by the construction is sufficient to accommodate successively therein: i) any level to be positioned above a tower stump built in a conventional manner, ii) an assembly to be positioned at the top of the tower, b) a crane mounted on the upper side of the structure, c) a lifting device with at least three supports which is connected with the structure or with the crane and has a load-bearing capacity which allows the structure and the crane to be lifted together, whereby the height difference to be overcome is at least equal to the height of the highest level to be mounted or to the height of the assembly to be mounted if it is higher than the highest level to be mounted, whereby the structure consists of at least three frames, each comprising a connecting frame section lying outside the tower volume, which connects an upper frame section and a lower frame section, whereby the upper frame sections of the at least three frames are connected to each other in a region of the tower axis, characterised in that the lower frame sections, which are lower by the height of the connecting frame sections, are designed as cantilevers being extendable into the direction of the tower axis, the extendable length of which is selected such that, irrespective of the diameter of a level, connections to the level are always realisable, whereby the lifting device is connected to the construction or to the crane mounted thereon. a) a structure being placeable at the top of the tower under erection and made of frames with several frame sections, which has a clear height and a clear width which are selected as large that the free space spanned by the construction is sufficient to accommodate successively therein: i) any level to be positioned above a tower stump built in a conventional manner, ii) an assembly to be positioned at the top of the tower, i) any level to be positioned above a tower stump built in a conventional manner, ii) an assembly to be positioned at the top of the tower, b) a crane mounted on the upper side of the structure, c) a lifting device with at least three supports which is connected with the structure or with the crane and has a load-bearing capacity which allows the structure and the crane to be lifted together, whereby the height difference to be overcome is at least equal to the height of the highest level to be mounted or to the height of the assembly to be mounted if it is higher than the highest level to be mounted, whereby the structure consists of at least three frames, each comprising a connecting frame section lying outside the tower volume, which connects an upper frame section and a lower frame section, whereby the upper frame sections of the at least three frames are connected to each other in a region of the tower axis, characterised in that the lower frame sections, which are lower by the height of the connecting frame sections, are designed as cantilevers being extendable into the direction of the tower axis, the extendable length of which is selected such that, irrespective of the diameter of a level, connections to the level are always realisable, whereby the lifting device is connected to the construction or to the crane mounted thereon.