We study C/O white dwarfs with masses of 1.0 to 1.4 M _ { \odot } accreting solar-composition material at very high accretion rates .
We address the secular changes in the WDs , and in particular , the question whether accretion and the thermonuclear runaways result is net accretion or erosion .
The present calculation is unique in that it follows a large number of cycles , thus revealing the secular evolution of the WD system .

We find that counter to previous studies , accretion does not give rise to steady state burning .
Instead , it produces cyclic thermonuclear runaways of two types .
During most of the evolution , many small cycles of hydrogen ignition and burning build a helium layer over the surface of the white dwarf .
This He layer gradually thickens and progressively becomes more degenerate .
Once a sufficient amount of He has accumulated , several very large helium burning flashes take place and expel the accreted envelope , leaving no net mass accumulation .

The results imply that such a system will not undergo an accretion induced collapse , nor will it lead to a SN Type Ia , unless a major new physical process is found .