We study the multipole response of nuclei for situations in which the
neutron content becomes progressively rich. It is observed that the oc
currence of weakly bound states towards the neutron drip line gives ri
se to low-lying concentrations of strength in the continuum which are
not of a resonant character. These do not result from a redistribution
of the expected high-lying response, but rather amount to a significa
nt source of additional strength. The effect can be accounted for in t
erms of sum rules that grow - beyond a straightforward increase in the
number of particles involved - because of the large spatial extent of
the weakly bound orbitals.