We consider in this paper multiphase flow models involving two, three or four fields, in total mechanical and thermodynamical disequilibrium. Thus several pressure fields arise, and we precisely focus here on the pressure relaxation process, while restricting to four distinct multiphase flow models. The first two models only involve immiscible compressible components, while the last two hybrid models involve both miscible and immiscible components. It is shown that some -weak- restrictions may occur on pressure gaps, which are unlikely to appear in practice. Evenmore, three-phase flow models may involve a non-monotone behaviour in the return to pressure equilibrium.