Device and method for constant tension feeding, threads or yarns fed to textile or winding machine or metallic wire to similar machine, in discontinuously with phase sequences. The thread motion has at least first and second feeding or absorption states following each other in time. A controller, connected to a tension detector and thread accumulator, intervenes on the accumulator based upon tension value from the detector. A compensator, between the accumulator and tension detector, cooperates with thread to compensate variation of feeding or absorption state of the thread upon passage between each first and second feeding or absorption state. The controller intervenes to modify the accumulator's action on thread and maintain tension value detected by the detector at set value. Interaction between thread and compensator keeping constant tension value during the changing phase of the feeding state. The compensator freely moveable under action of thread relative to a resting position.