Abstract: The string of vehicles travelling on rails includes bodies (2, 3, 4) articulated together and wheel assemblies (8 to 11), wherein the orientation of the wheels can be adjusted to be tangent to the rails. To this end, an adjusting device includes sensors (40), which make is possible to measure the relative angles (.beta.1, .beta.2) between the longitudinal axes (31) of the bodies. A calculating unit (41) is designed for determining for each unitary vehicle (8 to 11) the variable angle (.alpha.1, .alpha.2, .alpha.3, .alpha.4) between a direction perpendicular to the axes (37) of the wheels and the longitudinal axis (31) of the body concerned, from the values of the relative angles (.beta.1, .beta.2) measured and, preferably, in combination with the angular speed of rotation of the bodies around their vertical axis, measured with gyroscopic sensors provided on the bodies. An adjusting member in the form of a jack then adjusts the orientation of the wheels according to the variable angles calculated.