Several constant-flux filtration experiments for yeast cell suspensions, yeast cell debris, and dodecane-water emulsion were performed at various operating conditions in both hat-sheet and tubular-membrane systems. The aim of the paper is two-fold. Firstly the relationship between constant-Aux behaviour and membrane fouling is discussed. In some cases constant-flux filtration was realized at a constant transmembrane pressure which was below a critical value. In general constant-flux : filtration was obtained with moderately increasing transmembrane pressure, and this approach is shown to have some advantages over normal constant-pressure filtration because it clearly provides for the possibility of avoiding over-fouling and so reduces the severity of fouling. Secondly, the concept of critical flux is introduced. Whilst it has long been recognised that low-pressure microfiltration is much more effective than high-pressure microfiltration, the emphasis in this work is upon the possible existence of a critical flux and the desirability of starting filtration operations at a low flux. The critical-flux hypothesis is that on start-up there exists a flux below which a decline of flux with time does not occur. Equations which may enable identification of the appropriate flux level are included.