An eddy current contactless braking system for decelerating long products (bi), such as bars, exiting from a rolling mill configured to manufacture said long products (bi), said system comprising: at least one braking module comprising a multiplicity of electromagnets arranged in a series along a braking line (lb), each of said electromagnets being configured to induce a magnetic field (B) and comprising an open magnetic core and a coil around said magnetic core , wherein the open magnetic core comprises a gap formed by two opposed poles between which said magnetic field (B) flows, the electromagnets of said braking module being configured in a way that the gap of each open magnetic core is apt to receive and let contactlessly slide therethrough each long product (bi) exiting from said rolling mill ; and in a way that a braking magnetic force (Fd) is exercised on said long product (bi) by said electromagnets when said long product (bi) contactlessly slides through said gap, said braking magnetic force (Fd) being opposite to the direction of movement of said long product (bi) exiting from said rolling mill characterized in that for any braking module the electromagnets are staggeredly disposed along said braking line (lb) according to a first row and to a second row so as to form an alternate arrangement with each other along said braking line (lb), wherein the electromagnets of said first row and the electromagnets of said second row are offset from each other in a direction transverse to said braking line (lb) in a way that all of the gaps formed by the two opposed poles of each magnetic core are lined up so that the contactless passage of a long product (bi) through the gaps of said series of electromagnets is enabled. at least one braking module comprising a multiplicity of electromagnets arranged in a series along a braking line (lb), each of said electromagnets being configured to induce a magnetic field (B) and comprising an open magnetic core and a coil around said magnetic core , wherein the open magnetic core comprises a gap formed by two opposed poles between which said magnetic field (B) flows, the electromagnets of said braking module being configured in a way that the gap of each open magnetic core is apt to receive and let contactlessly slide therethrough each long product (bi) exiting from said rolling mill ; and in a way that a braking magnetic force (Fd) is exercised on said long product (bi) by said electromagnets when said long product (bi) contactlessly slides through said gap, said braking magnetic force (Fd) being opposite to the direction of movement of said long product (bi) exiting from said rolling mill characterized in that for any braking module the electromagnets are staggeredly disposed along said braking line (lb) according to a first row and to a second row so as to form an alternate arrangement with each other along said braking line (lb), wherein the electromagnets of said first row and the electromagnets of said second row are offset from each other in a direction transverse to said braking line (lb) in a way that all of the gaps formed by the two opposed poles of each magnetic core are lined up so that the contactless passage of a long product (bi) through the gaps of said series of electromagnets is enabled. <EOS>