The present invention provides a differential pressure body suit with external support against body suit migration. In its preferred embodiment, such body suit may comprise a close-fitting, multi-layered suit sealed against a mammal's skin to contain the differential pressure, or a looser-fitting suit that bends at the mammal's joints with minimal force. External support means include either fixed or movable mechanical supports attached to the body suit, extraordinary air pressure levels for making the body suit rigid, or exoskeletons attached to the body suit. A cyclic control system can turn the differential pressure condition within the body suit on and off on a selective basis to accommodate the movement of the legs of the mammal.