The now extinct Pb-205 is a pure s-process radionuclide (t(1/2) = 1.5
10(7) y) of possible substantial cosmochemical interest. As a necessar
y complement to the detailed theoretical study of the nuclear physics
and astrophysics aspects of the Pb-205-Tl-205 pair carried out by Yoko
i et al. (1985), and to the recent calculation of the Pb-205 productio
n in Wolf-Rayet stars by Arnould et al. (1997), this paper addresses f
or the first time in some detail the question of the survival of this
radionuclide in thermally pulsing AGE stars. This problem is made diff
icult by the high sensitivity to temperature and density of the rates
of the weak interaction processes that are able to produce or destroy
Pb-205. In view of this sensitivity, a recourse to detailed stellar mo
dels is mandatory. With the help of some simplifying assumptions conce
rning in particular the third dredge-up characteristics, some of which
(like its depth) being considered as free parameters, predictions are
made for the Pb-205 contamination of the stellar surface at the end o
f a pulse-interpulse cycle following a series of a dozen of pulses in
three different intermediate-mass stars (M = 3 M-circle dot,Z = 0.02;
M = 6 M-circle dot,Z = 0.021 M = 3 M-circle dot,Z = 0.001). It is conc
luded that the chances for a significant Pb-205 surface enrichment are
likely to increase with M for a given Z, or to increase with decreasi
ng Z for a given M. More specifically, following the considered pulses
at least, the enrichment appears to be rather unlikely in the 3 M-cir
cle dot star with Z = 0.02, while it seems to be much more probable in
the other two considered stars. It is also speculated that the (3 M-c
ircle dot,Z = 0.02) star could possibly experience some Pb-205 en rich
ment following later pulses than the ones considered in this paper.