Several aspects of the numerical solution methods in RETRAN were investigated with the objective of improving or removing time-step size limitations. The investigations focused on the material transport Courant limit associated with the mixture energy equation. The initial development efforts are limited to the homogeneous equilibrium mixture model of two-phase flow. Some of the results are applicable to four- and five-equation two-phase flow models. The solution method improvements were developed and demonstrated by calculations with RETRAN.