In a double-caterpillar running gear in which an underbody (2) which bears the load and can be pivoted with respect to the said load about a perpendicular axis (6) is supported on two bearing points (4), arranged opposite one another in an axis (5) of rotation, of each caterpillar unit (1) and on a rocker (9) which in the normal position runs parallel to the connection line of the two bearing points (4) and is arranged so as to be capable of rotating about an axis which lies in the vertical longitudinal centre plane (8) and is mounted with its ends in each case in a caterpillar unit (1), an increase in stability is achieved by the underbody (2) being supported on the rocker (9) with the intermediate connection of in each case one hydraulic cylinder (14) at two bearing points (11) which are each arranged at the same distance from the axis lying in the longitudinal centre plane (8), and that the two hydraulic cylinders (14) can be connected to one another hydraulically. <IMAGE>