Fabric treatment machine, comprising - two or more fabric accumulation stations (11A, 11B) in succession, among which an initial accumulation station wherein the fabric is adapted to enter from the outside of the machine, with a first speed, and a final accumulation station from which the fabric is adapted to exit toward the outside of the machine, with the same said first speed, - a movement path between said accumulation stations (11A,11B) wherein the fabric is adapted to travel, - a device (16, 116, 216, 316) for the alternating movement of the fabric between two consecutive accumulation stations (11A, 11B), along said path, with a second movement speed greater than said first speed so as to alternately accumulate fabric on said two consecutive accumulation stations (11A,11B), - an electronic unit for controlling the machine, - for each of at least two consecutive accumulation stations (11A, 11B), an apparatus for managing the accumulation of fabric in the accumulation station, comprising - a device for evaluating the amount of fabric comprised in the relative station, so that, when said evaluation device detects an amount of fabric in the station below a limit threshold, a command is generated for reversing the movement of the fabric exiting from said station, - a device for detecting the tension of said fabric, therefore, when said evaluation device detects an amount of fabric in the station below a limit threshold, the device (16, 116, 216, 316) for the alternating movement of the fabric is commanded to reverse the motion of the fabric along said path, characterized in that an electronic program adapted to modify the value of said limit threshold based on said tensional state of the fabric detected by said device for detecting the tension is associated with said management apparatus, and wherein said electronic program is adapted to increase said limit threshold for the amount of fabric in the station by a predetermined value if, upon the detection of an amount of fabric below said limit threshold by said device for evaluating the amount of fabric, said device for detecting the tension of said fabric verifies a critical tensional state for said fabric. - two or more fabric accumulation stations (11A, 11B) in succession, among which an initial accumulation station wherein the fabric is adapted to enter from the outside of the machine, with a first speed, and a final accumulation station from which the fabric is adapted to exit toward the outside of the machine, with the same said first speed, - a movement path between said accumulation stations (11A,11B) wherein the fabric is adapted to travel, - a device (16, 116, 216, 316) for the alternating movement of the fabric between two consecutive accumulation stations (11A, 11B), along said path, with a second movement speed greater than said first speed so as to alternately accumulate fabric on said two consecutive accumulation stations (11A,11B), - an electronic unit for controlling the machine, - for each of at least two consecutive accumulation stations (11A, 11B), an apparatus for managing the accumulation of fabric in the accumulation station, comprising - a device for evaluating the amount of fabric comprised in the relative station, so that, when said evaluation device detects an amount of fabric in the station below a limit threshold, a command is generated for reversing the movement of the fabric exiting from said station, - a device for detecting the tension of said fabric, therefore, when said evaluation device detects an amount of fabric in the station below a limit threshold, the device (16, 116, 216, 316) for the alternating movement of the fabric is commanded to reverse the motion of the fabric along said path, - a device for evaluating the amount of fabric comprised in the relative station, so that, when said evaluation device detects an amount of fabric in the station below a limit threshold, a command is generated for reversing the movement of the fabric exiting from said station, - a device for detecting the tension of said fabric, therefore, when said evaluation device detects an amount of fabric in the station below a limit threshold, the device (16, 116, 216, 316) for the alternating movement of the fabric is commanded to reverse the motion of the fabric along said path, characterized in that an electronic program adapted to modify the value of said limit threshold based on said tensional state of the fabric detected by said device for detecting the tension is associated with said management apparatus, and wherein said electronic program is adapted to increase said limit threshold for the amount of fabric in the station by a predetermined value if, upon the detection of an amount of fabric below said limit threshold by said device for evaluating the amount of fabric, said device for detecting the tension of said fabric verifies a critical tensional state for said fabric.