Method for managing and controlling the feeding of a thread or yarn or a plurality of threads with constant tension and/or speed to a circular knitting machine or a stocking machine, said feeding being obtained according to the different operating steps of such circular knitting or stocking machine which are carried out during the production of a product, such production comprising a succession of said operating steps defining a complete production cycle, each thread or yarn or plurality of threads being fed to said circular knitting or stocking machine by a corresponding feeder device with constant tension and/or speed and/or controlled by a sensor device adapted to control the thread tension or speed, the identification of each single operating step of the production cycle of the circular knitting or stocking machine being carried out through a synchronization signal generated by the circular knitting or stocking machine, said method being characterized in that: - every single operating step produces a specific part of the product, said single operating step being identified through the generation of a unique synchronization signal by the circular knitting or stocking machine at the start or at the end of the production of the specific part of the product, - particular and set values of said thread or yarn tension or the thread or yarn speed being associated to each of such operating steps, said set values being recorded in a table; - such values being memorized in setting and control means to which such feeder device and sensor (1, 100) are connected; and - said setting and control means intervening on the aforementioned feeder device and sensor device to define the values of said thread or yarn tension or speed of the fed and controlled thread or yarn corresponding to the memorized values for obtaining said specific part of the product, - said unique synchronization signal being used by said setting and control means for acting on each feeder device and sensor to allow said feeder and sensor to control and/or feed the thread or yarn or plurality of threads, with the characteristics suitable to implement said single operating step to obtain said specific part of the product, said setting and control means uniquely identifying said single operating step according to the unique synchronization signal received from the circular knitting or stocking machine, the implementation of said single operating step to obtain the specific part of the product being carried out according to the above particular and set values of the thread or yarn tension or the thread or yarn speed controlled by each feeder device and sensor (1, 100) for each of such operating steps. - every single operating step produces a specific part of the product, said single operating step being identified through the generation of a unique synchronization signal by the circular knitting or stocking machine at the start or at the end of the production of the specific part of the product, - particular and set values of said thread or yarn tension or the thread or yarn speed being associated to each of such operating steps, said set values being recorded in a table; - such values being memorized in setting and control means to which such feeder device and sensor (1, 100) are connected; and - said setting and control means intervening on the aforementioned feeder device and sensor device to define the values of said thread or yarn tension or speed of the fed and controlled thread or yarn corresponding to the memorized values for obtaining said specific part of the product, - said unique synchronization signal being used by said setting and control means for acting on each feeder device and sensor to allow said feeder and sensor to control and/or feed the thread or yarn or plurality of threads, with the characteristics suitable to implement said single operating step to obtain said specific part of the product, said setting and control means uniquely identifying said single operating step according to the unique synchronization signal received from the circular knitting or stocking machine, the implementation of said single operating step to obtain the specific part of the product being carried out according to the above particular and set values of the thread or yarn tension or the thread or yarn speed controlled by each feeder device and sensor (1, 100) for each of such operating steps.