A fibre fabric cutting system comprising a first conveying assembly including a first endless conveyor belt guided in an endless loop along a first curved path and drivable to move in a first conveying direction along the first curved path, the first curved path comprising a cutting section in which, in an operating position of the fibre fabric cutting system, the first conveyor belt extends in the horizontal direction, a fibre fabric supply unit adapted to receive a web of fibre fabric and operable to supply the web to the cutting section such that when the first conveyor belt is moved in the first conveying direction the web is transported by the first conveyor belt along the cutting section, and a cutting unit disposed near the cutting section and adapted to be operable to cut a web of fibre fabric into sheets, which web is supplied to the cutting section by the fibre fabric supply unit and transported by the first conveyor belt when moving into the first conveying direction, characterized in that the first conveying assembly further includes a second endless conveyor belt guided in an endless loop along a second curved path and drivable to move in a second conveying direction along the second curved path, wherein the first curved path and the second curved path are arranged such that when the first and second conveyor belts (5, 7) are driven to move in the first and second conveying directions (9, 11), respectively, they cooperate to define for sheets cut by the cutting unit a first transport path comprising a plurality of vertically spaced levels (25, 27, 29, 31, 63) extending transversely to the vertical direction and arranged one above the other, the cutting section defines the first level and each of the subsequent levels (27, 29, 31, 63) is defined by a section of at least one of the first and second curved paths of the first and the second conveyor belts (5, 7) in which the respective conveyor belt (5, 7) extends in a direction transversely to the vertical direction, and sheets transported along the first transport path move from one level (25, 27, 29, 63) to the next level (27, 29, 31, 63) starting with the first level, wherein they are supported alternately against the gravitational force by the first and the second conveyor belt (5, 7) on consecutive levels (25, 27, 29, 31, 63). a first conveying assembly including a first endless conveyor belt guided in an endless loop along a first curved path and drivable to move in a first conveying direction along the first curved path, the first curved path comprising a cutting section in which, in an operating position of the fibre fabric cutting system, the first conveyor belt extends in the horizontal direction, a fibre fabric supply unit adapted to receive a web of fibre fabric and operable to supply the web to the cutting section such that when the first conveyor belt is moved in the first conveying direction the web is transported by the first conveyor belt along the cutting section, and a cutting unit disposed near the cutting section and adapted to be operable to cut a web of fibre fabric into sheets, which web is supplied to the cutting section by the fibre fabric supply unit and transported by the first conveyor belt when moving into the first conveying direction, characterized in that the first conveying assembly further includes a second endless conveyor belt guided in an endless loop along a second curved path and drivable to move in a second conveying direction along the second curved path, wherein the first curved path and the second curved path are arranged such that when the first and second conveyor belts (5, 7) are driven to move in the first and second conveying directions (9, 11), respectively, they cooperate to define for sheets cut by the cutting unit a first transport path comprising a plurality of vertically spaced levels (25, 27, 29, 31, 63) extending transversely to the vertical direction and arranged one above the other, the cutting section defines the first level and each of the subsequent levels (27, 29, 31, 63) is defined by a section of at least one of the first and second curved paths of the first and the second conveyor belts (5, 7) in which the respective conveyor belt (5, 7) extends in a direction transversely to the vertical direction, and sheets transported along the first transport path move from one level (25, 27, 29, 63) to the next level (27, 29, 31, 63) starting with the first level, wherein they are supported alternately against the gravitational force by the first and the second conveyor belt (5, 7) on consecutive levels (25, 27, 29, 31, 63).