A multiple-spindle turning machine has an upright structure supporting a rotary drum which, in turn, supports a plurality of workpiece supporting spindles. On the upright, at each spindle, a cross slide adapted to support a plurality of machining tools to be used for machining the front portion of a workpiece is provided. The machine tool further comprises, in front of the rotary drum, parallel guides which are arranged crosswise of the machine bed, on the guides being slidably mounted two slides each including a workpiece supporting spindle. On the two sides of the machine tool, near each spindle, a vertical slide adapted to support a plurality of machining tools for machining the rear portion of the workpiece is arranged.