A major part of the computational effort in chemical process simulation and compositional reservoir simulation is spent by phase equilibrium calculations: phase split and phase stability analysis. The calculation algorithms must be efficient and highly robust. The reduction methods offet an attractive alternative to conventional methods. Several recent papers have questioned on the efficiency of the reduction methods as compared to conventional methods, concluding that reduction methods become faster than conventional ones starting from a certain number of components. In this work, besides evaluating the computational effort required by various conventional and reduction formulations, the efficiency (per iteration and global) of stability testing and flash calculations is evaluated separately, the condition of the linear system of equations is analyzed, as well as the influence of symmetry properties and of the linear solver. Some important links are formally established between conventional and reduced methods and between different reduction methods. Numerical experiments carried out with several mixtures confirm that flash calculations using the reduction methods are more efficient than conventional methods only for mixtures with many components (more than 20) and few non-zero binary interaction parameters; this means that reduction methods for phase split are suitable for process simulation (mixtures may contain hundreds of components), but there are not suitable for compositional simulation, where the number of components is limited, typically to a dozen. On the contrary, for phase stability testing, it is shown that reduction methods are more efficient than conventional ones even for mixtures with few components, thus they are suitable for compositional simulation. This observation is very important since, in most compositional reservoir simulators, no explicit phase split is required, flash calculations being part of a larger problem (coupled with flow equations), while phase stability testing must be performed in most grid blocks. (C) 2014 Elsevier B.V. All rights reserved.