Mathematical models of the time-dependent behavior of two-phase natural-circulation loops were used to predict the operation and to explain the unusual instability sometimes observed. The initial results obtained for a loop similar to the Univ. of Minnesota loop were used to formulate a more complex and accurate model, and the predicted transient behavior was in close agreement with the experimental results from the Minnesota loop. For a 300 psia, high-pressure loop, unstable oscillatory behavior was predicted under certain conditions and stable behavior under others. Closed unstable regions rather than limits were predicted, and the specifications of stability in terms of a single parameter were found to be impossible. The great difference in oscillatory frequencies observed at low and high pressures was found to be due largely to the system geometry. The criterion for the absence of oscillations was found to be similar to one of the criteria for stability of chemical reaction systems.