Symbiotic binaries are systems containing white dwarfs (WDs) and red giants. Symbiotic novae are those systems in which thermonuclear eruptions occur on the WD components. These are to be distinguished from events driven by accretion disk instabilities analogous to dwarf novae eruptions in cataclysmic variable outbursts. Another class of symbiotic systems are those in which the WD is extremely luminous and it seems likely that quiescent nuclear burning is ongoing on the accreting WD. A fundamental question is the secular evolution of the WD. Do the repeated outbursts or quiescent burning in these accreting systems cause the WD to gain or lose mass? If it is gaining mass, can it eventually reach the Chandrasekhar Limit and become a supernova (a SN Ia if it can hide the hydrogen and helium in the system)? In order to better understand these systems, we have begun a new study of the evolution of Thermonuclear Runaways (TNRs) in the accreted envelopes of WDs using a variety of initial WD masses, luminosities and mass accretion rates. We use our 1-D hydro code, NOVA, which includes the new convective algorithm of Arnett, Meakin and Young, the Hix and Thielemann nuclear reaction solver, the Iliadis reaction rate library, the Timmes equation of state, and the OPAL opacities. We assume a solar composition (Lodders abundance distribution) and do not allow any mixing of accreted material with core material. This assumption strongly influences our results. We report here (1) that the WD grows in mass for all simulations so that canonical `steady burning' does not occur, and (2) that only a small fraction of the accreted matter is ejected in some (but not all) simulations. We also find that the accreting systems, before thermonuclear runaway, are too cool to be seen in X-ray searches for SN Ia progenitors
