Abstract <p>A system of four balance differential equations is used to describe dynamics of heterogeneous compressible binary mixtures with stiffened gas equations of state for the mixture’s components, including gas and liquid ones. The main points are its quasi-homogeneous form, which arises as a result of eliminating volume fractions of components from the collection of sought functions and the construction of a quadratic equation for the common pressure of components, as well as its subsequent regularization of the quasi-gasdynamic type. We present a description of the phase transition in the limit of instantaneous relaxation to thermodynamic equilibrium between components, whose implementation is reduced to solving nonlinear equations for the saturation temperature and pressure. In general, this approach is implemented by an explicit finite-difference scheme, which is two-level in time and symmetric three-point conservative in space, without limiters and with splitting with respect to physical processes (in the one-dimensional case). Using this scheme, test computations with the water–vapor phase transition are carried out.</p>