A 10 M(.) model of Population I composition is evolved from the hydrogen-burning main sequence to the thermally pulsing ''super''-asymptotic giant branch (TPSAGB) stage, where it has an oxygen-neon (ONe) core of mass 1.196 M(.) and is experiencing thermal pulses driven by helium-burning thermonuclear hashes. Interior abundance characteristics are relevant to an understanding of the core collapse of massive accreting white dwarfs in close binary star systems. At mass point 0.2 M(.), abundances by mass are X(O-16) = 0.656, X(Ne-20) = 0.215, X(Na-23) = 0.0467, X(Mg-24) = 0.0325, X(Mg-25) = 0.0115, X(C-12) = 0.0112, X(Ne-22) = 0.00893, X(Ne-21) = 0.00689, X(Mg-26) = 0.00560 and X(Al-27) = 0.00528. Abundances near the surface of the core are relevant to an understanding of nova outbursts in cataclysmic variables. At mass point 1.17 M(.), abundances by mass are X(O-16) = 0.511, X(Ne-20) = 0.313, X(Na-23) = 0.0644, X(Mg-24) = 0.0548, X(Mg-25) = 0.0158, X(Al-27) = 0.0108, X(C-12) = 0.00916, X(Mg-26) = 0.00989, X(Ne-21) = 0.00598, and X(Ne-22) = 0.00431. Carbon burning is quenched at the beginning of the thermally pulsing phase, and a layer of CO matter of mass similar to 0.015 M(.) separates the ONe core from overlying helium- and hydrogen-rich layers. The outer 0.01 M(.) of the CO layer contains essentially no neon: very little new Ne-20 has been made, and most of the Ne-22 which has been made from the original CNO elements has been converted into Mg-25 and neutrons which have been captured to form neutron-rich isotopes. If the observational counterpart of the model is in a close binary and fills its Roche lobe near the end of the carbon-burning phase, and if the binary evolves into a cataclysmic variable, one expects that the ejecta of approximately 1000 nova outbursts will exhibit an underabundance of neon and overabundance of carbon oxygen, and magnesium. During the TPSAGB phase, characteristics of a pulse cycle approach local limit-cycle values after similar to 30 pulses. Helium-shell flashes are of about the same strength (L(He)(max) similar to 3 x 10(6) L(.), L(He)(min) similar to 100 L(.)) as in AGB models with CO cores of mass similar to 1 M(.), but the time between flashes (similar to 200 yr) and the mass of helium fuel built up between hashes (similar to 1.3 x 10(-4) M(.)) are much smaller. The amount of energy released in a flash is not enough to propel matter at the hydrogen-helium discontinuity far enough outward that associated cooling extinguishes hydrogen burning (L(H)(min) similar to 10(2) L(.) L(H)(max) similar to 6 x 10(4) L(.)). The temperature at the base of the convective shell forced by helium burning attains a maximum of T-CSB(max) similar to 360 x 10(6) K. Depending on the choice of cross section for the Ne-22(alpha, n)Mg-25 reaction, 50%-80% the Ne-22 initially in the convective shell is converted into Mg-25, providing 20-30 neutrons for every Fe-56 seed nucleus. The neutron density (similar to 6 x 10(12) cm(-3)) is presumably much larger than is appropriate for producing s-process isotopes in the solar system distribution at critical branch points. During pulse powerdown, at least 7% and perhaps as much as 30% of the matter which has been in the convective shell is dredged up into the convective envelope. Thus, an observational counterpart of the model may exhibit an enhancement of heavy s-process isotopes in a nonsolar distribution and Mg isotopes in a distinctly nonsolar distribution, but because of the large mass of the convective envelope, these anomalies may not be detectable in a typical TPSAGB star. The abundance of Li relative to H in a model may be much larger or much smaller than Li/H similar to 10(-10) depending on the treatment of convection and on where the model is in the TPSAGB phase. At the beginning of the TPSAGB phase, the surface abundances by number of CNO elements are in the ratio (C:N:O) = (2.4:4.3:6.3), compared with the initial ratios (C:N:O) = (3.6:1.0:8.0). During the TPSAGB phase, the ratio of C to N decreases, and the ratio of C-12 to C-13 decreases from similar to 25 to similar to 4. a test of these predictions involves abundance estimates of the brightest long-period variables in the Galaxy and in the Magellanic Clouds. Perhaps the major signature of a TPSAGB star is a brightness greater than the ''classical limit'' of M(bol) = -7.1. Betelgeuse in our Galaxy and four stars in the Magellanic Clouds are brighter than the supposed limit, but they exhibit abundance characteristics which can be accounted for in the framework of TPSAGB theory. Assuming that a superwind removes mass from the surface at a rate of similar to 10(-4) M(.) yr(-1), the final mass of the ONe white dwarf formed by our TPSAGB model is similar to 1.26 M(.), the outer 0.06 M(.) of which is composed primarily of carbon and oxygen.
