Double spherical dressing apparatus for grindstone includes cutting table slidably mounted at right angles to axis of rotation of grindstone. Swing shaft is journaled within main assembly and assembly is attached to cutting table for sliding motion along path parallel to the axis of grindstone. Swing table is connected to rotate with and relative to swing shaft. Shaft table carries dresser tool and tool rotates about axis of swing shaft and swing table to dress peripheral faces of grindstone.