Computation of compressible two-phase flows with single-pressure single-velocity two-phase models in conjunction with the moving grid approach is discussed in this paper. A HLLC-type scheme is presented and implemented in the context of Arbitrary Lagrangian–Eulerian formulation for solving the five-equation models. In addition, the extension to multicomponent cases is also examined. The method is first assessed on a variety of Riemann problems including both fixed and moving grids applications showing its simplicity and robustness. The method is also tested on 2-D moving mesh applications including fluid–structure interactions. The heat and mass transfer modeling is finally examined for two-phase mixtures. Computations using a fractional step approach of water hammer and fast depressurization with flashing are performed. Good agreement is obtained with available experimental data. All computations are performed with the Europlexus fast transient dynamics software.