An assembly for adjusting the rails (9a, 9b) of a railway track to be made, comprising a first carriage for determining a shimming plan, the first carriage being movable along a section of the railway track, said section being provided with a plurality of baseplates (8a, 8b) for receiving the rails of the track section, the first carriage comprising: - a first chassis, which is automotive; - first positioning means (31, 32, 33) of the first carriage, which enable an absolute position of the first chassis to be measured; and - baseplate detection means (41a, 41b) which allow a relative position of each baseplate of the track section to be determined with respect to the first chassis, the assembly further comprising first calculation means programmed to establish a shimming plan for the track section on the basis of a track plan of the railway to be made and of the absolute positions of each baseplate of the track section, the absolute position of a baseplate being determined on the basis of the relative position of the said baseplate and of the absolute position of the chassis, characterised in that it comprises a second carriage for pre-positioning shims on the rail-receiving baseplates of the track section, according to the shimming plan for said track section determined by means of the first calculation means, the second carriage comprising: - a second chassis, which is automotive; - second positioning means (51, 52) of the second carriage, which make it possible to measure an absolute position of the second chassis; - a reservoir, which contains a plurality of horizontal and/or vertical shims of different thicknesses; and, - feeding means (61a, 61b), suitable for selecting a suitable shim from the reservoir and placing it on the baseplate above which the second carriage is located, the assembly further comprising second calculation means capable of reading the shimming plan taking into account the absolute position of the second chassis and of controlling the feeding means by indicating the shim to be selected. - a first chassis, which is automotive; - first positioning means (31, 32, 33) of the first carriage, which enable an absolute position of the first chassis to be measured; and - baseplate detection means (41a, 41b) which allow a relative position of each baseplate of the track section to be determined with respect to the first chassis, the assembly further comprising first calculation means programmed to establish a shimming plan for the track section on the basis of a track plan of the railway to be made and of the absolute positions of each baseplate of the track section, the absolute position of a baseplate being determined on the basis of the relative position of the said baseplate and of the absolute position of the chassis, characterised in that it comprises a second carriage for pre-positioning shims on the rail-receiving baseplates of the track section, according to the shimming plan for said track section determined by means of the first calculation means, the second carriage comprising: - a second chassis, which is automotive; - second positioning means (51, 52) of the second carriage, which make it possible to measure an absolute position of the second chassis; - a reservoir, which contains a plurality of horizontal and/or vertical shims of different thicknesses; and, - feeding means (61a, 61b), suitable for selecting a suitable shim from the reservoir and placing it on the baseplate above which the second carriage is located, - a second chassis, which is automotive; - second positioning means (51, 52) of the second carriage, which make it possible to measure an absolute position of the second chassis; - a reservoir, which contains a plurality of horizontal and/or vertical shims of different thicknesses; and, - feeding means (61a, 61b), suitable for selecting a suitable shim from the reservoir and placing it on the baseplate above which the second carriage is located, the assembly further comprising second calculation means capable of reading the shimming plan taking into account the absolute position of the second chassis and of controlling the feeding means by indicating the shim to be selected.