The conceptual design of the pellet suspension reactor, PSR, which is absolutely passively safe against LOCA and LOFA accidents, is discussed elsewhere. The dynamics of a continuously fuelled pellet suspension reactor based on an isothermal and non-linear description of neutron-nuclide interactions, an considered herein. Also, the stability studies have already taken place for this on-line fuelled system and for this purpose analysis is done by application of the Hurwitz criteria. We find that, in general and for a plausible range of operational refueling conditions, such systems are absolutely stable.