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Reactor dynamics and system stability studies are performed on a conceptual burst mode Gaseous Core Reactor (GCR) space nuclear power system. This concept operates on a closed Brayton Cycle in the burst mode (on the order of 100 MW output for a few thousand seconds) using a disk Magnetohydrodynamic (MHD) generator for energy conversion. The fuel is a gaseous mixture of UF4 or UF6 and helium. Dynamic analysis is performed using circulating fuel, point reactor kinetics equations along with thermodynamic, lumped parameter heat transfer and 1-D isentropic flow equations. The gaseous nature of the fuel plus the fact that the fuel is circulating leads to dynamic behavior which is quite different from that of conventional solid core systems. For the examined transients, Doppler fuel temperature and moderator temperature feedbacks are found to be insignificant when compared to reactivity feedback associated with fuel gas density variations.