If the accreting white dwarf increases its mass to the Chandrasekhar mass, it will either explode as a Type I supernova or collapse to form a neutron star. In fact, there is a good agreement between the exploding white dwarf model for Type I supernovae and observations. We describe various types of evolution of accreting white dwarfs as a function of binary parameters (i.e, composition, mass, and age of the white dwarf, its companion star, and mass accretion rate), and discuss the conditions for the precursors of exploding or collapsing white dwarfs, and their relevance to cataclysmic variables. Particular attention is given to helium star cataclysmics which might be the precursors of some Type I supernovae or ultrashort period X-ray binaries. Finally we present new evolutionary calculations using the updated nuclear reaction rates for the formation of O+Ne+Mg white dwarfs, and discuss the composition structure and their relevance to the model for neon novae.
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