For exothermic fluid-phase reactions, a reactor which is cooled at the wall can exhibit multiplicity or parametric sensitivity. Moreover, for heterogeneously catalysed exothermic fluid-phase reactions, each of the catalytically active pellets in the reactor can exhibit multiplicity. Both forms of multiplicity can lead to thermal instability and as such have to be taken into account in reactor design. Here the effect of both instabilities is quantified. To this end, simple first-order kinetics are assumed, and intraparticle resistances and reactor and particle dynamics are not considered. A one-dimensional model, consisting of microscale mass and heat balances, is chosen to describe the reactor. It is assumed that the fluid inlet temperature equals the coolant temperature. The pellet scale model is a combined mass and heat balance for the pellet and it assumes that the Chilton¿Colburn analogy holds. For its incorporation in the reactor model it is assumed that for every individual pellet heat removal to neighbouring pellets via the mutual contact spots is negligible as compared to the heat transferred to the surrounding fluid. Consequently every pellets is isolated from its neighbours. In the thermally most critical region, i.e. the hot-spot region, reactor stability is determined by three parameter groups: a dimensionless adiabatic temperature rise, an Arrhenius number or dimensionless activation temperature and the ratio of the number of heat transfer units to the number of reaction units. For pellet multiplicity, a fourth parameter group becomes significant in addition: the ratio of the reaction rate to the pellet mass transfer rate. This number depends on the pellet size. A general recipe is given which enables us to determine whether or not pellet thermal instability can become important in reactor operation. For the situation where it is significant, generalized diagrams are presented indicating which pellet sizes problems must be expected due to pellet multiplicity.