Abstract: The machining center serves for grinding workpieces with complex shaped surfaces, such as turbines or jet engine blades. One or several workpieces are clamped in a workpiece chucking device. The latter is displaceable along an X and a Y axis. Additionally, each workpiece is clamped rotatably around its longitudinal axis. A support device is disposed on a stand, and is displaceable along a vertical Z axial direction. One or several automatically exchangeable grinding attachments are inserted in support device. Each grinding attachment comprises grinding means driveable from support device. The support device is inclinable around an axis of inclination, which runs parallel to the Y axis. Each grinding attachment is rotatable by any angle around a grinding attachment longitudinal axis, which runs parallel to the Z axis when the support device is in the uninclined state. All said axes are numerically controlled.