Flow rate, ramp (constant rate of temperature rise), and package density are recognized to be particularly important for obtaining uniform uptake in the package dyeing of acrylic fibre yarns. This paper is concerned with the contribution of these three parameters to levelness in this system. An attempt is made to define empirical mathematical relationships between these variables and the observed rate of dyeing, in order to be able to specify those values of these parameters which would be expected to give rise to unlevel dyeings.Linear relationships were ,found between these parameters and the rate oj cxhaustion per circulation of the dyebath, expressed either as the overall rate or as separate rates for the two successive stages of the exhaustion process (attributed to adsorption at the surface of the fibre and diffusion into the interior). The equations relating rate of exhaustion to package density, ramp and the reciprocal of the rate of liquor flow can be combined into a single equation. This enables the relative effects of these variables to be calculated. For example, the equation can be used to decide which combination o f ramp and flow rate will give a pre-determined rate o f exhaustion by a package ofgiven density. In a similar way, the correspondirig equation relating the instrumental criterion o.f degree of unlcvelness to package density, ramp and rate of pow forms a convenient means of predicting the effects that tlrese three variables will have on the possibility that unlevel dyeing will occur.