Method of monitoring the concentricity of a tool, which can be rotated about the Z axis, of an NC machine tool by means of a proximity sensor, wherein the tool and the proximity sensor can be moved relative to one another along the X, Y and Z axes, characterized by the following steps: (a) recording of a distance characteristic curve of the proximity sensor with respect to the tool at a predetermined Z position (Z 0) of the tool by relative movement of the tool and the proximity sensor in a direction extending at right angles to the tool axis; and either positioning of the tool with respect to the proximity sensor at a predetermined measuring position (X 0, Y 0, Z 0) and storing the measuring signals of the proximity sensor in a plurality of different rotary positions of the tool as reference signals, and for concentricity control of the tool: renewed positioning of the tool with respect to the proximity sensor at the predetermined measuring position (X 0, Y 0, Z 0), determining a difference between the current measuring signals of the proximity sensor in the plurality of different rotary positions of the tool and the stored reference signals, determining a concentricity deviation (Δd) based on the distance characteristic curve from the difference, and checking the tool when a predetermined concentricity deviation has been exceeded; or positioning of the tool with respect to the proximity sensor at a predetermined measuring position (X 0, Y 0, Z 0) and storing the distances of the tool with respect to the proximity sensor, determined from these measuring signals by means of the distance characteristic curve, in a plurality of different rotary positions of the tool as reference distances; and for concentricity control of the tool: renewed positioning of the tool with respect to the proximity sensor at the predetermined measuring position (X 0, Y 0, Z 0), determining a concentricity deviation (Δd) from the difference between the actual distances of the tool with respect to the proximity sensor determined from the current measuring signals by means of the distance characteristic curve in the plurality of different rotary positions of the tool, and the stored reference distances, and checking the tool when a predetermined concentricity deviation has been exceeded. (a) recording of a distance characteristic curve of the proximity sensor with respect to the tool at a predetermined Z position (Z 0) of the tool by relative movement of the tool and the proximity sensor in a direction extending at right angles to the tool axis; and either positioning of the tool with respect to the proximity sensor at a predetermined measuring position (X 0, Y 0, Z 0) and storing the measuring signals of the proximity sensor in a plurality of different rotary positions of the tool as reference signals, and for concentricity control of the tool: renewed positioning of the tool with respect to the proximity sensor at the predetermined measuring position (X 0, Y 0, Z 0), determining a difference between the current measuring signals of the proximity sensor in the plurality of different rotary positions of the tool and the stored reference signals, determining a concentricity deviation (Δd) based on the distance characteristic curve from the difference, and checking the tool when a predetermined concentricity deviation has been exceeded; or renewed positioning of the tool with respect to the proximity sensor at the predetermined measuring position (X 0, Y 0, Z 0), determining a difference between the current measuring signals of the proximity sensor in the plurality of different rotary positions of the tool and the stored reference signals, determining a concentricity deviation (Δd) based on the distance characteristic curve from the difference, and checking the tool when a predetermined concentricity deviation has been exceeded; positioning of the tool with respect to the proximity sensor at a predetermined measuring position (X 0, Y 0, Z 0) and storing the distances of the tool with respect to the proximity sensor, determined from these measuring signals by means of the distance characteristic curve, in a plurality of different rotary positions of the tool as reference distances; and for concentricity control of the tool: renewed positioning of the tool with respect to the proximity sensor at the predetermined measuring position (X 0, Y 0, Z 0), determining a concentricity deviation (Δd) from the difference between the actual distances of the tool with respect to the proximity sensor determined from the current measuring signals by means of the distance characteristic curve in the plurality of different rotary positions of the tool, and the stored reference distances, and checking the tool when a predetermined concentricity deviation has been exceeded. renewed positioning of the tool with respect to the proximity sensor at the predetermined measuring position (X 0, Y 0, Z 0), determining a concentricity deviation (Δd) from the difference between the actual distances of the tool with respect to the proximity sensor determined from the current measuring signals by means of the distance characteristic curve in the plurality of different rotary positions of the tool, and the stored reference distances, and checking the tool when a predetermined concentricity deviation has been exceeded.