In this study the feasible operation and stability of a special boiling-slurry reactor (BSR), in which a single exothermic chemical reaction occurs, are determined. Its feed consists of a nonvolatile liquid reactant dissolved in an inert solvent and gaseous reactants, while the effluent consists only of gaseous components. The BSR attains a unique steady state within a bounded range of operating conditions, the boundaries of which are defined by simple algebraic expressions. While the unique steady states are usually locally stable, they are not always globally stable. For example, when the start-up temperature is too low, the reactor may not reach the steady state and instead reach a "fill-up" state. In that state the liquid volume continuously increases, while the concentrations and temperature remain essentially constant. For some sets of start-up temperatures two distinct fill-up states may exist. When the start-up liquid volume and temperature are very high, a "dry-up" state may exist so that the liquid continuously decreases, while the reactor temperature and concentration remain essentially constant. This state eventually will shift the reactor to the unique steady state. Dry-up, fill-up, and a steady state coexist in some parts of the feasible operation region, thus requiring a special start-np procedure. The BSR may exhibit sustained oscillations for some parameter sets.