SUMMARY:Many applications of fibres require a stabilization of their shape if subjected to thermal and mechanical treatments. This can be achieved by equilibration of the structure of a fibre annealed at a given form. With regard to the process of thermosetting of a fibre one has to distinguish between the retention of a desired form under the action of compelling forces and the free relaxation of the fibre to its equilibrium shape. The degree of set depends on the annealing conditions, and in the former case also on the extent of cooling.The possibilities for a technically made fibre (far from equilibrium) to arrange its structure during a subsequent annealing step can be used for the stabilization of the fibre form. Generally, the dissipative structure then disproportionates in relaxed regions of higher entropy and crosslinking domains of lower internal energy depending on the conditions of annealing (heating rate, temperature, humidity of the material, annealing time, and applied stress). For the relaxed regions one has to assume not only a deorientation of molecular segments but also a decrease of inter-