  We discuss the linear response of the Bogolyubov theory of a weakly
interacting Bose gas below the critical temperature. The specific aspects, due
to induced perturbation terms in the self-consistent treatment are discussed in
detail. We show that Bogolyubov's model having a gap-less equilibrium spectrum
nevertheless gives rise to an effective susceptibility which does not satisfy
the super-fluidity criterion of Hohenberg and Martin.
