the track position actually realized immediately after tamping operation and designated here as desired initial track position 31 of the track 3 this initial track position 31 is measured by the measuring car 14 immediately after tamping and clearly shows long wave geometrical track errors persons skilled in the art will understand that the measurement by the car 15 may also be carried out by a separate track measuring car data determined by the car 15 may be suitably transmitted for example wireless to the immediately trailing track stabilizer 20 or the data may be transmitted by diskette or modem the transmitted data are inputted into a computer 32 located on the track stabilizer 20 subsequently a conventional electronic compensation and factorizing process computes from the determined track ordinates 30 long wave corrective values 35 for correction of the cross level and lateral track position of the track 3 the determined corrective values 35 enable the track stabilizer 20 to precisely carry out the subsequent track stabilization by scanning the track on three points and alignment of the track in response to the predetermined corrective values and desired track ordinates i e the track stabilizer 20 is able to carry out simultaneously with lowering of the track for countering the initial settling of.