This paper presents a study of pressure and velocity relaxation in two-phase flow calculations. Several of the present observations have been made elsewhere, and the purpose of the paper is to strengthen these observations and draw some conclusions. It is numerically demonstrated how a single-pressure two-fluid model is recovered when applying instantaneous pressure relaxation to a two-pressure two-fluid model. Further, instantaneous velocity relaxation yields a drift-flux model. It is also shown that the pressure relaxation has the disadvantage of inducing a large amount of numerical smearing. The comparisons have been conducted by using nalogous numerical schemes, and a multi-stage centred (MUSTA) scheme for non-conservative two-fluid models has been applied to and tested on the two-pressure two-fluid model. As for others, previously tested two-phase flow models, the MUSTA schemes have been found to be robust, accurate and non-oscillatory. However, compared to their Roe reference schemes, they consistently have a lower computational efficiency for problems involving mass transport.