A supporting device for a plurality of adapter chucks for the precision grinding or polishing of optical components comprises a spindle shaft having a central bore for supplying one of a gas and a vacuum, at least one arm adjustably supported by a head of the spindle shaft and having a seating for an adapter chuck, and a flexible vacuum/gas line provided between the seating and the spindle shaft. The arm is adjustable as to its angle of inclination relative to an axis of the spindle shaft.