In a recently published paper in JMLR, Tsang et al. (2005) present an algorithm for SVM called Core Vector Machines (CVM) and illustrate its performances through comparisons with other SVM solvers. After reading the CVM paper we were surprised by some of the reported results. In order to clarify the matter, we decided to reproduce some of the experiments. It turns out that to some extent, our results contradict those reported. Reasons of these different behaviors are given through the analysis of the stopping criterion.