Abstract: A numerically controlled grinding machine for grinding workpieces, such as tools, and other metallic or ceramic elements, comprises a machine bed (1) having fixedly connected to it a rigid, distortion-free portal (9) which has a reinforcing rear wall (13) rigidly connected to the machine bed, two side stands (10) and a horizontal bridge (11) which extends at a distance above the machine bed (1). A double wheel grinding spindle carrier (20) is adjustably mounted on the portal (9) for positioning along at least one axis (-y). The machine bed (1) projects at one side from the portal (9). The machine bed (1) supports a workpiece carrier movable about a plurality of axes.