A nonlinear model is developed for the xenon induced flux oscillation problem that occurs in nuclear power plants. The model is based on Galerkins' method of weighted residuals applied to multigroup diffusion theory. A similar linear model is developed by the same methods in order to consider the effects of the nonlinearities of the system. The effects of multi- and single-energy group considerations are also examined. Finally, the effects of various number of basis functions used to approximate the flux, iodine, and xenon concentrations is determined. A partial listing of the computer program XORA, developed from the nonlinear and linear models, is given along with representative input and output from this program. / Ph. D.