Fuel element for a pressurized water reactor and method for producing cladding tubes

A fuel element for a pressurized water reactor is described. The fuel element contains a laterally open skeleton having control-rod guide tubes each with a first end and a second end, spacers fastened to the control-rod guide tubes, a fuel element head disposed at the first end of the control-rod guide tubes, and a fuel element foot disposed at the second end of the control-rod guide tubes. Gastight cladding tubes are inserted into the skeleton and each is filled with a column of fuel pellets. At least some of the gastight cladding tubes have a multilayer wall. The multilayer wall is formed of a mechanically stable matrix containing a first zirconium alloy disposed in a middle of the multiplayer wall; and a thinner protective layer of a second zirconium alloy alloyed to a lesser extent than the first zirconium alloy. The thinner protective layer is bound metallurgically to the matrix and is disposed on an inside of the matrix facing the fuel pellets.