We prove that the coefficient of the longitudinal part of the W-boson
propagator close to resonance is equal to 1/(M(W)2 +iepsilon(L)), wher
e epsilon(L) is proportional to squares of masses of those fermions th
at the W can decay to. Consequently, the full propagator has a non-g(m
unu) part that differs from the commonly used form, even in the limit
of vanishingly small fermion masses.