The relation between a linear series and thermal (i.e. secular) stability of stellar models is discussed. Models of accreting degenerate dwarfs are considered as an example of transition from instability to stability. This transition occurs while the accretion rate increases. Such models are relevant for novae and symbiotic stars.

I shall limit this presentation to the secular i.e. thermal instabilities of stellar models in the hydrostatic and thermal equilibria. The time dependence of a small perturbation of an equilibrium model is assumed to be exponential, but the eigenvalues do not have to be real. In general they are complex. That means that thermal instability, if present, may either lead to an exponential growth of a perturbation, or may lead to oscillations with a growing amplitude. The complex nature of the eigenvalues makes a search for them difficult and no general prescription is available for a search to be complete and successful. However, a search for real eigenvalues is much easier. Some information about the presence of purely exponential modes may be achieved even without searching for them by means of calculating a linear series of stellar models. I shall describe this concept in this communication.