  The 19F production during the first dozen thermal pulses of AGB stars with
(M=3,Z=0.02), (M=6,Z=0.02) and (M=3,Z=0.001) is investigated on grounds of
detailed stellar models and of revised rates for 15N(a,g)19F and 18O(a,g)22Ne.
These calculations confirm an early expectation that 19F {\it is} produced in
AGB thermal pulses. They also enlarge substantially these previous results by
showing that the variations of the level of 19F production during the evolution
is very sensitive to the maximum temperature reached at the base of the pulse.
These variations are analyzed in detail, and are shown to result from a subtle
balance between different nuclear effects (mainly 19F production or destruction
in a pulse, and 15N synthesis during the interpulse), possibly super-imposed on
dilution effects in more or less extended pulse convective tongues. Our
calculations, as most others, do not predict the third dredge-up self-
consistently. When parametrized, it appears that our models of
intermediate-mass AGB stars are able to account only for the lowest 19F
overabundances observed in solar-metallicity MS, S and C stars. That conclusion
is expected to hold true for low-mass stars when F production results from
secondary 13C only. Massive AGB stars, on the other hand, are not expected to
build up large surface F abundanc- es. Therefore, the large F overabundance
reported for the super Li-rich star WZ Cas (where HBB is supposed to be
operating) remains unexplained so far. Our results for the (M=3,Z=0.001) star
indicate that F surface overabundances can also be expected in low-metallicity
stars provided that third dredge-ups occur after the early cool pulses. The
relative increase in the surface 19F/12C ratio is, however, lower in the
low-metallicity than in the solar-metallicity star. No observations are
