Abstract: The vehicle--e.g. a wheelchair--has groups of wheels (10) mounted on a spider (9) for rotation about a central axis to enable the vehicle to ascend or descend stairs or steps. To reduce the risk of the vehicle rolling off the steps, each wheel has alongside it a foot member (further wheel 13), rigidly secured to the spider, with engagement portions (18) to engage the stair when the spider is tilted and clear portions (14) allowing free rolling when the spider is level. Also, a geared drive arrangement to the spider(s) is provided to give braking or restraint with a mechanical advantage. In a further embodiment the drive motor for rotating the spiders is mounted on a pivoted projecting arm or skid (27, FIG. 6) which transmit the motor or braking torque directly to the stairs to reduce the risk of the vehicle tipping.