The dynamics of two-phase flow through the coolant channels of a natural-circulation boiling-water nuclear reactor is studied analytically. One-dimensional conservation equations describing the flow through each channel are written in the linearized perturbed form, and Laplace transformation in time is performed. A systematic procedure is developed to approximate the solution. The solution may, in general, be oscillatory both in time and in space. Since the space dependence of the transient steam void fraction is available, it may be multiplied by its reactivity worth to obtain the space-time-dependent void reactivity. The transfer function expressing the relation between the void fraction or velocity of water and the heat flux may be conveniently used to understand the hydrodynamic stability. The analytical techniques developed are applicable to both natural- and forced-circulation systems.