It has been proposed that the mass of theZ0 boson should be defined as the real part, and the width of theZ0 as the imaginary part of the complex poleMc, for the reason thatMc is gauge invariant (g.i.). Clearly, this definition is only useful if we can calculate theS-matrix up to some accuracy in a g.i. way. This is not at all obvious, since the use of theZ0 dressed propagator mixes up the order of the diagrams, and thus order by order gauge invariance of theS-matrix, in this formulation, becomes an ill-defined concept.