A numerical control apparatus for controlling a numerical lathe has a superimposing Z-axis control function in which, when a work is machined by the control of movement of a tool holder in the Z2- and X2-axis directions driving movement of a spindle in the Z1-axis direction, the variance of the position of the spindle in the Z1-axis direction as detected by a Z1-axis position detector is added to the value derived from a Z2-axis position detector which detects the position of the tool holder in the Z2-axis direction, and the position of the second tool holder in the Z2-axis direction is controlled using the result of the addition as the feedback value of the Z2-axis position of the second tool holder. According to this arrangement, the variance of the position of the spindle in the Z1-axis direction is always added to the detection value of the tool holder position in the Z2-axis direction, thus producing the same effect as that produced by an arrangement in which tool holders and Z2-axis driving mechanism and X2-axis driving mechanism for controlling the positions of these tool holders are carried by the spindle so that the tool holders, as well as the Z2-axis and X2-axis driving mechanisms are automatically moved in accordance with the movement of the spindle in the X1-axis direction.