An eccentric grinder has a housing provided with a gear rim an eccentrically rotating grinding disc provided with a gear rim which rolls on the gear rim of the housing and in operation without load provides an additional rotary movement of the grinding disc. The gear rim of the grinding disc is a friction rim so that in operation without load there is a minimum slippage and in operation under load there is a maximum slippage of the rims relative to one another. The gear rim of the housing is fixed to the housing and includes a toothed rim which is formed by a ring-shaped toothed belt with a toothing while the gear rim of the grinding disc has a plurality of projections which incompletely engage in the toothing of the gear rim of the housing and therefore an elastic deformation of the projections gives the grinding disc a shaking movement with partial meshing under maximum slippage.