The dye uptake of Terylene (TCI) subjected to dry and live‐steam heat can be characterised by a constant defined as the uptake divided by the square root of time (A/t), as in equations for diffusion. This constant is found to decrease to a minimum with increase in temperature of dry heating and then to increase to a value greater than that for the unheated yarn at high temperatures of preheating. Steam preheating also affects the constant and, at the higher temperatures of steam heating, shows similar tendencies to those found for dry heat but to a less extent. These results were obtained under conditions that allow free shrinkage during dyeing. However, if dyeing is carried out with the material under tension, although the general tendency is the same, the dye‐uptake constant is greater than that for the corresponding samples dyed in the absence of tension and is greater than that of the unheated yarn for most of the samples. Measurement of parameters indicative of structural changes in fibres, e.g. moisture regain, density, X‐ray orientation and X‐ray lateral order, shows that these variations in dyeing properties cannot be explained on the basis of a fringe‐micellar network theory of structure. An explanation is advanced which postulates a structure with rod‐like morphological units separated by narrow voids, the size, amount and tortuosity of which govern the accessibility of the dye.