The balancing construction is applicable to a machine tool of the type including an upright column movably supported on a bed, a saddle movable vertically along the column, and a headstock displaceable laterally of the column while being guided by the headstock. The saddle is connected to a respective balance weight by a pair of flexible connecting elements trained over pulleys on the opposite ends of a pair of arms supported on top of the column. A pair of suspension arms are mounted on the upper end of the column for oscillation in a horizontal plane about a vertical pivot axis at one end of each suspension arm, the pivot axis including a tubular pivot. Respective conical rollers support each suspension arm for rolling over the top of the column during the horizontal oscillation, and the two arms are interconnected for movement parallel to each other. Each arm has a pulley at each end, and a pair of flexible connectors are trained over these pulleys to connect the headstock to a respective balance weight movable vertically of the column. These latter flexible connecting elements extend vertically through the tubular pivot axes of the respective arms. A synchronizing mechanism interconnects the headstock to the two suspension arms to synchronize the horizontal oscillation of the suspension arms with a lateral displacement of the headstock.