A tube bending apparatus comprises an elongated mandrel having a length at least three times the length of a tube to be bent in the apparatus. A first mandrel holder is arranged at the rear end of the mandrel and a second mandrel holder is forwardly spaced from said first by a distance slightly greater than the length of a tube. Each of the mandrel holders comprises a pair of clamping jaws and a fluid operated cylinder-and-piston unit connected to each clamping jaw for alternatingly moving the clamping jaws of the first and the second mandrel holder between a closed position engaging the mandrel and an open position permitting a tube about the mandrel to be moved in axial direction by a plurality of transport rollers into an axially movable slide provided with a clamping collet so that a tube clamped in the region of the rear end thereof by the clamping collet is during forward movement of the slide moved into a bending mechanism arranged in the region of the front end of the mandrel and bent during operation of the bending mechanism. The bent tube is pushed out in forward direction from the mandrel while the collet is open as a second tube located between the second mandrel holder and the slide is moved into the latter to be clamped by the collet and a third tube located between the mandrel holders is transported between the slide and the second mandrel holder while the latter is opened and the first mandrel holder is closed.