A honing machine has at least one clamping unit that clamps a workpiece and has a rotary drive for the workpiece. A spindle unit has a stroke drive for an inner honing tool for inner honing of the workpiece. An outer honing device that is movable relative to the workpiece in an axial direction of the workpiece is provided. The outer honing device has several honing stones and an advancing device acting on the honing stones. The honing stones each are advanced in a radial direction relative to the workpiece. The advancing device has at least one linear drive for each one of the honing stones and a common drive motor for all of the linear drives.