Matter of solar system composition has been added to the surfaces of t
wo initially cool carbon-oxygen (GO) white dwarfs of masses 0.5 M-. an
d 0.8 M-. at rates in the range 10(-8) to 10(-6) M-. yr(-1). Four diff
erent regimes are encountered. (1) At the highest accretion rates, mod
els become red giants after the accretion of only a very small amount
of mass. As the accretion rate is decreased, models are encountered th
at (2) burn hydrogen at the same rate at which it is accreted, (3) exp
erience a series of nondynamical hydrogen shell flashes followed event
ually by a powerful helium shell flash, and, finally, (4) experience n
ova-like hydrogen shell flashes. Although all of the regimes have been
explored, special attention has been given to models that experience
recurrent mild hydrogen-burning pulses or burn hydrogen at a stationar
y rate. For lower accretion rates, the helium flash is so powerful tha
t the convective layer forced by helium burning penetrates deeply into
the hydrogen-rich envelope; this penetration may lead to the ejection
of external layers even if the helium flash would not of itself have
become dynamical. For higher accretion rates, even when convection doe
s not penetrate into hydrogen-rich layers, the helium layer expands, a
nd much, if not most, of the accreted matter is lost during the event
because of the interaction of the expanded envelope with the companion
star. Analysis of the results suggests that it is unlikely that, in t
he real world, a hydrogen-accreting CO white dwarf with a typical init
ial mass will attain the Chandrasekhar mass. Dynamical helium-burning
flashes are probable.