  The now extinct 205Pb is a pure s-process radionuclide (t_{1/2} = 1.5x10^7 y)
of possible substantial cosmochemical interest. As a necessary complement to
the detailed theoretical study of the nuclear physics and astrophysics aspects
of the 205Pb - 205Tl pair carried out by Yokoi et al. (1985), and to the recent
calculation of the 205Pb production in Wolf-Rayet stars by Arnould et al.
(1997), this paper addresses for the first time in some detail the question of
the survival of this radionuclide in thermally pulsing AGB stars. This problem
is made difficult by the high sensitivity to temperature and density of the
rates of the weak interaction processes that are able to produce or destroy
205Pb. In view of this sensitivity, a recourse to detailed stellar models is
mandatory. With the help of some simplifying assumptions concerning in
particular the third dredge-up characteristics, some of which (like its depth)
being considered as free parameters, predictions are made for the 205Pb
contamination of the stellar surface at the end of a pulse-interpulse cycle
following a series of a dozen of pulses in three different intermediate-mass
stars (M=3M_sun,Z=0.02; M=6M_sun,Z=0.02; M=3M_sun,Z=0.001). It is concluded
that the chances for a significant 205Pb surface enrichment are likely to
increase with M for a given Z, or to increase with decreasing Z for a given M.
More specifically, following the considered pulses at least, the enrichment
appears to be rather unlikely in the 3M_sun 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 (3M_sun,Z=0.02) star could possibly experience some 205Pb enrichment
following later pulses than the ones considered in this paper.
