A shaft comprising functional elements, such as an assembled camshaft for an internal combustion engine, a method for producing such shafts, and internal combustion engines equipped with such shafts. The functional elements each have a bore and are produced separately from the shaft main body, and the bore is subsequently press fit onto the shaft body to attach the functional element in an axially and rotationally fixed manner. The shaft is also provided with at least one roller bearing that includes at least one undivided roller bearing element which is mounted on the shaft body between two functional elements, for example, by press fitting.