Boiling water reactors (BWRs) are susceptible to thermal-hydraulic instabilities that must be considered in BWR design and operation. Early BWRs were designed to be very stable while operating under natural-circulation conditions. As reactor designs have been modified, stability margins have been reduced, and the potential for stability events, such as occurred at the La Salle and Vermont Yankee plants, has increased. These events and other considerations point to the need for a reliable analysis tool for predicting the dynamic behavior of these events. Transient thermal-hydraulic systems analysis codes have been used to analyze hydrodynamic instabilities, and although the results are often reasonable and exhibit the expected behavior, they are sensitive to changes in node and time-step size, and a converged solution cannot be demonstrated by reducing the node and time-step sizes. This sensitivity is due to numerical diffusion that limits the use of most time domain system analysis codes for BWR stability analyses since it directly affects the decay (or growth) ratio computed for stability events. A conservation equation transport model using the method of characteristics has been developed for use with the RETRAN-03 mixture energy and vapor continuity equations. The model eliminates numerical diffusion in the RETRAN solution. The development and validation of a conservation equation transport model for the RETRAN-03 time domain thermal-hydraulic analysis code that extends the range of application to simulating the dynamic behavior of stability events are presented. RETRAN-03 analyses are presented that compare simulations of hydrodynamic instability events with data.