Self-propelled civil engineering machine comprising a running gear which has wheels or other running-gear units (2, 3) which are at the front in the direction of working and wheels or other running-gear units (4, 5) which are at the rear in the direction of working, a chassis of the machine which is carried by the running gear, a drive arrangement for driving the front wheels or other running-gear units and/or the rear wheels or other running-gear units (2, 3; 4, 5), a steering arrangement for steering the front wheels or other running-gear units (3, 4) and/or the rear wheels or other running-gear units (4, 5), and a unit having controls, the chassis of the machine being designed to be adjustable in the heightwise direction and/or in inclination, characterised in that the civil engineering machine has an arrangement for assisting the driver of the machine when reversing, the arrangement for assisting the driver of the machine when reversing comprising: a unit for sensing the position of the front wheels or other running-gear units (2, 3) and/or rear wheels or other running-gear units (4, 5), a calculating unit for determining data ((x0, y0), (x1, y1), (x2, y2), (x3, y3), M, r) which defines at least one trajectory (T 1 to T 6) of the civil engineering machine as a function of the position of the front wheels or other running-gear units (2, 3) and/or the rear wheels or other running-gear units (4, 5), an image detecting unit for detecting an image of the rear part of the civil engineering machine, a display unit for displaying the detected image of the rear part of the civil engineering machine, and an image processing unit which is so designed that the at least one trajectory (T 1 to T 6) is superimposed on the image of the rear part of the civil engineering machine which is displayed on the display unit, the calculating unit comprising: means for calculating data ((x0, y0), (x1, y1), (x2, y2), (x3, y3), M) defining the at least one trajectory (T 1 to T 6), as a function of the position of the front wheels or other running-gear units (2, 3) and/or the rear wheels or other running-gear units (4, 5) in a co-ordinate system (x, y) referred to the running gear of the civil engineering machine, means for converting the data defining the at least one trajectory to be in a co-ordinate system (x', y') referred to the image detecting unit in which the image is displayed on the display unit, and means for correcting the data defining the at least one trajectory in the co-ordinate system (x', y') referred to the image detecting unit, on the basis of a correcting function by which allowance is made for a change in the longitudinal inclination and/or transverse inclination and/or height of the image detecting unit relative to the co-ordinate system (x, y) referred to the running gear of the civil engineering machine. a unit for sensing the position of the front wheels or other running-gear units (2, 3) and/or rear wheels or other running-gear units (4, 5), a calculating unit for determining data ((x0, y0), (x1, y1), (x2, y2), (x3, y3), M, r) which defines at least one trajectory (T 1 to T 6) of the civil engineering machine as a function of the position of the front wheels or other running-gear units (2, 3) and/or the rear wheels or other running-gear units (4, 5), an image detecting unit for detecting an image of the rear part of the civil engineering machine, a display unit for displaying the detected image of the rear part of the civil engineering machine, and an image processing unit which is so designed that the at least one trajectory (T 1 to T 6) is superimposed on the image of the rear part of the civil engineering machine which is displayed on the display unit, means for calculating data ((x0, y0), (x1, y1), (x2, y2), (x3, y3), M) defining the at least one trajectory (T 1 to T 6), as a function of the position of the front wheels or other running-gear units (2, 3) and/or the rear wheels or other running-gear units (4, 5) in a co-ordinate system (x, y) referred to the running gear of the civil engineering machine, means for converting the data defining the at least one trajectory to be in a co-ordinate system (x', y') referred to the image detecting unit in which the image is displayed on the display unit, and means for correcting the data defining the at least one trajectory in the co-ordinate system (x', y') referred to the image detecting unit, on the basis of a correcting function by which allowance is made for a change in the longitudinal inclination and/or transverse inclination and/or height of the image detecting unit relative to the co-ordinate system (x, y) referred to the running gear of the civil engineering machine.