In a section of a ballasted track that extends over a plurality of crossties, ballast is removed and crossties are removed. Crosstie blocks mounted in concrete slabs are inserted, lifted, and fastened to the rails. The rails are supported by temporary, vertically adjustable supports and adjusted. In an area that extends over a number of concrete slabs, infill concrete is filled in from the underground up to at least part of the height of the concrete slabs, and after the infill concrete has hardened, at least a part of each of the supports located between two respective concrete slabs is removed. The method allows the conversion to be carried out without changing the position of the rails. After the placement of the supports, the track is immediately operable again so that the relevant section need not remain closed until all method steps are completed.