Abstract: A damping support structure for preventing vibrations of an apparatus table supporting an apparatus for manufacturing ultra-high precision devices such as semiconductors and printed circuit boards. The apparatus table is supported in suspension by support members, with its apparatus mounting surface disposed at a low level. The support members are supported by stationary members through vertically extendible and contractible first air springs. Horizontally extendible and contractible second air springs are disposed between the stationary members and the apparatus table. The first and second air springs serve to mitigate vertical and horizontal vibrations of the apparatus table, respectively.