We focus here on the relaxation process in a class of two-phase flow models, considering first gas-liquid flows, and then liquid-vapour mixtures. The whole analysis enables to exhibit a few conditions on the flow in order to guarantee the time decay of some variables. The former may depend on initial conditions but also on equations of state within each phase. The present analysis aims at providing some better understanding of inner processes, and it is also useful for numerical purposes, as emphasized in appendix B. It is a sequel of paper [J.M. Hérard and G. Jomée, ESAIM Proc. Surv., 72:19–40, 2023] where the sole pressure relaxation process in some multiphase flow models is investigated.