A road construction machine for processing roadways, - with an automotive travelling mechanism with a steerable front axle of said travelling mechanism comprising at least one support wheel (2, 3) and two rear support wheels (4, 5); - with a working device which is mounted in or on the machine frame and is approximately flush with said machine frame on one side, namely its so-called zero side; - with a pivot unit comprising an articulation area formed by the machine frame and a pivot arm which carries the rear support wheel on the zero side at its one end and is pivotally articulated at its other end to the articulation area of the machine frame, the pivot unit being implemented in such a manner that it can be pivoted between an "outwardly pivoted position", in which the rear wheel, which is on the zero side, is pivoted outwardly to an outer end position parallel to the longitudinal direction of the machine frame, and an "inwardly pivoted position", in which the rear support wheel, which is on the zero side, is inwardly pivoted to an inward end position parallel to the longitudinal direction of the machine frame, and - with a pivot gear which controls the adjustment of the pivot unit between the "outwardly pivoted position" and the "inwardly pivoted position" about a pivot axis characterized in that the pivot gear is a spatial gear with a thrust member (21, 22) which is adjustable in the vertical direction, and that it comprises a deflection device which is implemented in such a manner that it deflects the vertical movement of the thrust member (21, 22) to a horizontal inwardly and outwardly pivoting movement of the pivot arm. - with an automotive travelling mechanism with a steerable front axle of said travelling mechanism comprising at least one support wheel (2, 3) and two rear support wheels (4, 5); - with a working device which is mounted in or on the machine frame and is approximately flush with said machine frame on one side, namely its so-called zero side; - with a pivot unit comprising an articulation area formed by the machine frame and a pivot arm which carries the rear support wheel on the zero side at its one end and is pivotally articulated at its other end to the articulation area of the machine frame, the pivot unit being implemented in such a manner that it can be pivoted between an "outwardly pivoted position", in which the rear wheel, which is on the zero side, is pivoted outwardly to an outer end position parallel to the longitudinal direction of the machine frame, and an "inwardly pivoted position", in which the rear support wheel, which is on the zero side, is inwardly pivoted to an inward end position parallel to the longitudinal direction of the machine frame, and - with a pivot gear which controls the adjustment of the pivot unit between the "outwardly pivoted position" and the "inwardly pivoted position" about a pivot axis characterized in that the pivot gear is a spatial gear with a thrust member (21, 22) which is adjustable in the vertical direction, and that it comprises a deflection device which is implemented in such a manner that it deflects the vertical movement of the thrust member (21, 22) to a horizontal inwardly and outwardly pivoting movement of the pivot arm.