Machine for the production of cardboard tubes, comprising a mandrel (M) on which a cardboard tube (T) is formed by the helicoidal winding of a cardboard strip (S) on said mandrel (M); a winding member (WB) adapted to interact with the mandrel (M) and the cardboard strip (S) to realize said helicoidal winding, an inlet section for drawing-in the cardboard strip (S); dragging means adapted to drag the cardboard strip (S) introduced in said inlet section, along a predetermined dragging direction (TD), said dragging means being active during a drawing-in step; cutting means for configuring the cardboard strip (S) in a configuration suitable for winding it on the mandrel (M); and guide means adapted to guide the cardboard strip (S) towards the mandrel (M) at the end of said drawing-in step, said guide means being disposed and acting between the dragging means and the mandrel (M).