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 .