One of the important design considerations in modern water-cooled nuclear reactors is their thermal performance during hypothetical accident situations. However, an accurate analysis of the system thermal-hydraulics is required before the thermal margins can be appraised. In this paper, an analysis based on the method of characteristics has been developed by which the exact solution to flow decay transients in homogeneous two-phase systems can be obtained. The exact solution presented yields the system flow and quality at each point in space and time during an exponential flow decay transient. These parameters can then be combined with an appropriate CHF correlation to predict the occurrence of transient CHF.