In this paper we consider a model for pool-boiling systems known from the literature.This model involves only the temperature distribution within the heater and models the heatexchange with the boiling medium via a nonlinear boundary condition imposed on the fluid-heaterinterface. The model allows multiple homogeneous (i.e. spatially constant) and multipleheterogeneous steady-state solutions. The structure of this family of steady-state solutions has been studiedby means of a bifurcation analysis in two recent papers (Speetjens et al (2006a), Speetjens et al (2006b)). Thepresent study concentrates on stability properties of these steady-state solutions. To this end, a genericlinear and a case-specific nonlinearstability analysis are performed which show that only the homogeneous steady-state solutions ofcomplete nucleate or complete film boiling are linearly stable. All heterogeneous steady-state solutions appearlinearly unstable. These stability results are consistent with laboratory observations.