  It is pointed out that the usual threshold anomaly, found operative in the
energy behavior of the imaginary and real parts of the optical potential
representing the elastic scattering of tightly bound nuclei at near- and
below-barrier energies, suffers a drastic qualitative change in the case of the
elastic scattering of weakly bound nuclei. Owing to the strong coupling to the
breakup channel even at sub-barrier energies, the imaginary potential strength
seems to increase as the energy is lowered down to below the natural, barrier,
threshold, accompanied by a decrease in the real potential strength. This
feature is consistent with the dispersion relation. The system $^{6}$Li +
$^{208}$Pb is analyzed to illustrate this new phenomenon.
