Model studies have been performed on a cylindrical Gaseous Core Fission Reactor, combining neutron kinetics and gas dynamics. The calculations show that autonomous density oscillations of the fuel gas are possible, provided that the value of the Cp/CV ratio K of the fuel gas is in the correct range. These (in case of absence of an energy extraction mechanism) increasing oscillations are desired when the kinetic energy of the moving (ionized) gas is to be (directly) extracted in the form of electrical energy by induction or magneto-hydrodynamics.