Abstract: An automatic tool changer in which tools carried by an indexable magazine are brought to a tool transfer station, from which a first one of two independently pivoted transfer arms of a tool transfer mechanism takes the tool from the magazine and -- by X axis translation of the transfer mechanism -- carries that tool to a tool-ready position close to the spindle, but held in an inverted position. Upon completion of the operation being performed by the tool in the spindle, and stopping of the spindle, the transfer mechanism is given Y axis translation and additional X axis translation, to bring the pivot axis of the two transfer arms to a spindle transfer position in which the second transfer arm is in position to swing in an arc tangent to the spindle axis, so that -- upon 180.degree. of such swinging motion -- this second transfer arm is brought into position to grasp the tool in the spindle and, by swinging in the opposite direction, withdraw the tool from the spindle and hold it in an inverted position.