Methods and apparatuses are disclosed for laterally restraining a movable partition. In one embodiment, a movable partition includes two laterally spaced structures wherein each structure includes a plurality of hingedly coupled panels. A lateral restraint mechanism is located and configured to prevent lateral displacement of one or both of the two laterally spaced structures. In one embodiment, a cable is disposed between and extends from along the lower edge of the two laterally spaced structures. The cable is maintained in tension, at least while the partition is in a deployed condition, to prevent or minimize the lateral displacement of one or both of the structures such as when a draft or other external force acts on the structures. In one embodiment, the cable may be operatively associated with one or more drive components used to displace the movable partition. In another embodiment, the cable may be coupled to a take-up mechanism.