Current research treats the ATM paradigm as a generalization of multitude of concepts in the telecommunication area. On the other hand, fuzzy logic concepts are being applied in various engineering areas. This paper describes an application of fuzzy logic inference engine to buffer occupancy control in ATM networks. A model of statistical multiplexers of video sources for ATM networks is presented. We investigate the impact that the multiplexer's buffer capacity and the varying numbers of video sources have on the probability of cell loss. A conventional two-threshold and a fuzzy control mechanisms are considered, and their performance is compared. The features of these two controllers are observed for different update intervals and different propagation delays of the control signal.