The goal of this paper is to explore the low-frequency oscillations of arterial pressure in humans, also called Mayer waves. We carefully describe the cardiovascular control system in order to analyse how its different components may be involved in the occurrence of sustained oscillations. We carry out an analysis of stability leading to the definition of a stability index, which we use to study the influence of each control parameter on the stability of the cardiovascular system. We show that all major components of the control system are probably implicated in the appearance of Mayer waves, substantiating recent clinical results in human as well as experimental findings in rats.