Improving the existing technological processes of processing complex threads on knitting machines and looms requires determining the change in relative tension in the areas of refueling. The change of tension occurs due to the interaction of complex threads with guides of large curvature, taking into account and without taking into account the radial coverage of the complex thread by the surface of the guide. The task of determining the tension should be based on the use of dichotomy algorithm software in computer determination of the tension of complex threads. Determining the change in relative tension in the areas of filling of complex threads on knitting machines and looms, taking into account and without taking into account the radial coverage of the complex thread by the guide surface, will improve the technology of production of knitwear and fabrics. Improvement of technological processes of the knitting and textile industry should be based on complex researches of process of interaction of complex threads with directing surfaces of big curvature. Obtaining theoretical dependences will allow to obtain equations for determining the tension of the thread in the area of fabric formation and knitwear, reduce the percentage of thread breaks, improve the quality of finished products. Many studies do not take into account the nonlinear relationship between force and coefficient of friction in obtaining the final equations. All this leads to significant differences between theoretical and experimental dependences, which does not allow the use of the former in specific calculations. Downtime of technological equipment associated with the elimination of cliffs is 75-80% of the total downtime. It is possible to significantly reduce the number of breaks by using quality raw materials and optimizing the conditions of thread processing on knitted and textile machines, where their interaction with the guides and working bodies of great curvature takes place. The tension dependences of complex threads have the form of a system of transcendental equations, for the solution of which it is necessary to use numerical methods. The dichotomy method is the most effective.