Apparatus for laser or plasma cutting of pieces from laminar material wound on coils, comprising: - a cutting station, provided with at least one laser or plasma cutting head movable within an operative cutting area, which is placed between an entrance and an exit (10") of the laminar material into and out of said station in a longitudinal advancement direction of said material and is obtained above a receiving cavity of the cutting swarf of the laminar material; - means (21, 22, 23) for positioning a portion of said laminar material in said operative area on a cutting plane (m) placed above said receiving cavity, wherein said positioning means (21, 22, 23) are suitable to maintain said portion of laminar material blocked on said cutting plane (m) during the cutting operations, suspended in the air and longitudinally stretched over said receiving cavity; - a support structure which is arranged downstream of said cutting station and which defines a support plane for the laminar material leaving the cutting station, and - an electronic control unit responsible for controlling the operation of said apparatus; characterized in that said positioning means comprise three distinct locking devices (21, 22, 23), each of which is susceptible to act by reversibly locking on a transverse portion of the laminar material and to be passed through by a portion of laminar material placed on said cutting plane (m), wherein said three devices (21, 22, 23) are arranged in sequence along said longitudinal advancement direction inside the cutting station, wherein a first device is arranged in the proximity of said entrance, a second device is arranged in proximity of said exit (10") and a third device is arranged between said first and said second devices (21, 22), of the three locking devices (21, 22, 23) at least said third device being movable along said longitudinal advancement direction in the space comprised between said first and second device (21, 22), and in that said electronic control unit is programmed to coordinate the actuation of the three locking devices (21, 22, 23) in locking and in unlocking on the laminar material, in such a way that a portion of the laminar material inside the cutting station can be kept under tension on the cutting plane (m) by combining the action of the first locking device with the third device or with the second locking device, it being possible thereby to free the translation of the third locking device with respect to said portion of laminar material, while continuing to maintain the latter under tension. - a cutting station, provided with at least one laser or plasma cutting head movable within an operative cutting area, which is placed between an entrance and an exit (10") of the laminar material into and out of said station in a longitudinal advancement direction of said material and is obtained above a receiving cavity of the cutting swarf of the laminar material; - means (21, 22, 23) for positioning a portion of said laminar material in said operative area on a cutting plane (m) placed above said receiving cavity, wherein said positioning means (21, 22, 23) are suitable to maintain said portion of laminar material blocked on said cutting plane (m) during the cutting operations, suspended in the air and longitudinally stretched over said receiving cavity; - a support structure which is arranged downstream of said cutting station and which defines a support plane for the laminar material leaving the cutting station, and - an electronic control unit responsible for controlling the operation of said apparatus; characterized in that said positioning means comprise three distinct locking devices (21, 22, 23), each of which is susceptible to act by reversibly locking on a transverse portion of the laminar material and to be passed through by a portion of laminar material placed on said cutting plane (m), wherein said three devices (21, 22, 23) are arranged in sequence along said longitudinal advancement direction inside the cutting station, wherein a first device is arranged in the proximity of said entrance, a second device is arranged in proximity of said exit (10") and a third device is arranged between said first and said second devices (21, 22), of the three locking devices (21, 22, 23) at least said third device being movable along said longitudinal advancement direction in the space comprised between said first and second device (21, 22), and in that said electronic control unit is programmed to coordinate the actuation of the three locking devices (21, 22, 23) in locking and in unlocking on the laminar material, in such a way that a portion of the laminar material inside the cutting station can be kept under tension on the cutting plane (m) by combining the action of the first locking device with the third device or with the second locking device, it being possible thereby to free the translation of the third locking device with respect to said portion of laminar material, while continuing to maintain the latter under tension.