An apparatus for making a butt connection between tubular bodies, in particular between tubular cores for coils of wound material, comprising: - a connection station; - tubular body feed means arranged to position a first tubular body and a second tubular body in alignment with each other with a front end portion (3") of said second tubular body adjacent to a rear end portion of said first tubular body at a connection position of said connection station; - a rotation means (31,62) for rotating said first tubular body and said second tubular body integrally to each other and about a common longitudinal axis at said connection position; wherein said connection station comprises: - a adhesive tape slide supplier arranged to expose a free edge of said adhesive tape towards said connection position; - a slide supplier actuation means (63',63") arranged to bring said slide supplier closer to said connection position, and to bring said free edge to said connection position, such that, by operating said rotation means (31,62), said free edge is dragged by said rotating tubular bodies (1',1) and it adheres on said tubular bodies (1',1), thereby creating said butt connection of said tubular bodies, wherein said front end portion (3") is connected to said rear end portion, forming a connected tubular body; - a cut means for cutting said adhesive tape; - a tape-tensioning means (74,65) for creating a predetermined tension of said adhesive tape while said free edge is being dragged, such that, by bringing said cut means into contact with said adhesive tape stretched while said free edge is being dragged, said adhesive tape is cut, thereby creating a new free edge that is exposed towards said connection position; wherein said slide supplier comprises a roll of said adhesive tape, said roll rotatably arranged about an own rotation axis, characterised in that said tape tensioning means comprises a tape-retaining means (74,65, β) for retaining said adhesive tape arranged outside of said roll of said adhesive tape. - a connection station; - tubular body feed means arranged to position a first tubular body and a second tubular body in alignment with each other with a front end portion (3") of said second tubular body adjacent to a rear end portion of said first tubular body at a connection position of said connection station; - a rotation means (31,62) for rotating said first tubular body and said second tubular body integrally to each other and about a common longitudinal axis at said connection position; - a adhesive tape slide supplier arranged to expose a free edge of said adhesive tape towards said connection position; - a slide supplier actuation means (63',63") arranged to bring said slide supplier closer to said connection position, and to bring said free edge to said connection position, such that, by operating said rotation means (31,62), said free edge is dragged by said rotating tubular bodies (1',1) and it adheres on said tubular bodies (1',1), thereby creating said butt connection of said tubular bodies, wherein said front end portion (3") is connected to said rear end portion, forming a connected tubular body; - a cut means for cutting said adhesive tape; - a tape-tensioning means (74,65) for creating a predetermined tension of said adhesive tape while said free edge is being dragged, such that, by bringing said cut means into contact with said adhesive tape stretched while said free edge is being dragged, said adhesive tape is cut, thereby creating a new free edge that is exposed towards said connection position;