An adapter is disclosed for mounting a tool on an oscillating drive having a drive shaft that can be driven to oscillate about its longitudinal axis, wherein the adapter is passed by a central opening, and has at its drive end at least one positive-locking element for positive connection with the tool, the positive-locking element having the shape of a regular polygon, or a plurality of positive-locking elements arranged on a circle concentric to the center axis, or a plurality of outwardly extending convex projections having rounded tips and being connected with neighboring projections via rounded concave lateral flanks, wherein the positive-locking elements on the drive end are configured for positive-locking connection with a matching positive-locking counter-element on the drive shaft, and wherein the adapter has a second receptacle on its tool end for effecting connection with a tool having a shape different from the first receptacle and being configured as a circle, or as a plurality of positive-locking elements arranged along a circle concentric to the center axis, or as plurality of outwardly extending convex projections with rounded tips and being connected with neighboring projections via rounded concave lateral flanks.