An analysis of the scientific literature on project cash flow control and fuzzy modelling shows that project cash flows are modelled using only basic approaches drawn from fuzzy theory, which may distort the credibility of the model. In this paper, we therefore propose to use the whole spectrum of fuzzy arithmetic, and to select operations that suit the nature of the cash flows in question, their dependencies and the preferences of the project manager. An analysis of the literature also shows that in practically all existing models of project costs and cash flow management, project costs and cash flows are treated at a very high level of generality (without considering the various types of project, factors influencing their variability and signals warning of imminent cash-related problems), and estimations are not updated on an ongoing basis throughout the duration of the project. The results of a survey performed with the participation of 100 project managers show that this simplistic view of project cash flows may be distorting, and cannot guarantee the development of an efficient project cost and cash flow control system. We propose an approach that at least partially compensates for these drawbacks: it differentiates between types of project cash flows and the factors and triggers affecting changes in cash flows. Two case studies are used for a an initial verification of the approach. The paper concludes with suggestions for further research perspectives.