An investigation of the stability of a nuclear power reactor subject to random macroscopic parameter variations is performed. An analysis procedure for determining the effect of stochastic coefficients on the stability in the mean and mean square of linear systems is presented. The procedure is based on Gaussian white process variations which can be shown to be governed by the Fokker-Planck equation. Moment equations are extracted from the Fokker-Planck equation and serve as system equations used for the stability analysis. It is shown that for some simple space-independent reactor models it is possible for random macroscopic parameter variation to destabilize in the mean and mean square a deterministically stable system. Conversely, the study has shown that under certain conditions random macroscopic variation of system parameters can also stabilize in the mean and mean square, a system which is deterministically unstable. A coupled-core spatial reactor model is utilized for the investigation of xenon instability. The results of this analysis again indicate that random macroscopic parameter variation can be a stabilizing or destabilizing influence. Analog simulations of linear systems with stochastic coefficients and a simple reactor model are used to verify the analysis procedure developed in this research.