Anti-theft system for securing products inside a defined space, the system comprising: - at least one tag provided with an electronic chip capable of transmitting a first signal in a repetitive manner and generated in a first technology, which is the BLE technology (Bluetooth Low Energy) and in which the first signal consists of a sequence of advertising frames in BLE format, the signal only capable of being received within a limited perimeter around the tag, the tag being connected to a product on display by a disconnectable mechanical connection, the signal comprising information which allows the product to be identified, - an electronic transmitting device, installed at a fixed position within said perimeter, the device being capable of receiving the first signal when the device is located within said perimeter, and of sending, in a repetitive manner, a second signal capable of being received outside the perimeter and generated in a second technology that is different from the first technology, the second signal comprising at least the information for identifying the product as well as a value related to the distance between the tag and the transmitting device, and - at least one fixed or portable computer, configured such that it receives the second signal and provided with a digital application which is configured such that it manages, on the basis of said second signal, the presence of the tag within a defined security zone around the transmitting device, the fixed or portable computer further being configured such that it carries out a procedure for pairing the TAG by producing a direct link according to the first technology with the TAG without passing via the electronic transmitting device, when the electronic chip is operating in a so-called connectable mode, for BLE tags, the procedure for pairing being carried out by producing a direct link between the portable device and the tag, a link, without passing via the electronic transmitting device, the BLE tag operating in connectable mode during the procedure for pairing, after the pairing has been carried out, the tag switching to non-connectable mode in order to prevent a new connection and therefore a new pairing. - at least one tag provided with an electronic chip capable of transmitting a first signal in a repetitive manner and generated in a first technology, which is the BLE technology (Bluetooth Low Energy) and in which the first signal consists of a sequence of advertising frames in BLE format, the signal only capable of being received within a limited perimeter around the tag, the tag being connected to a product on display by a disconnectable mechanical connection, the signal comprising information which allows the product to be identified, - an electronic transmitting device, installed at a fixed position within said perimeter, the device being capable of receiving the first signal when the device is located within said perimeter, and of sending, in a repetitive manner, a second signal capable of being received outside the perimeter and generated in a second technology that is different from the first technology, the second signal comprising at least the information for identifying the product as well as a value related to the distance between the tag and the transmitting device, and - at least one fixed or portable computer, configured such that it receives the second signal and provided with a digital application which is configured such that it manages, on the basis of said second signal, the presence of the tag within a defined security zone around the transmitting device, the fixed or portable computer further being configured such that it carries out a procedure for pairing the TAG by producing a direct link according to the first technology with the TAG without passing via the electronic transmitting device, when the electronic chip is operating in a so-called connectable mode, for BLE tags, the procedure for pairing being carried out by producing a direct link between the portable device and the tag, a link, without passing via the electronic transmitting device, the BLE tag operating in connectable mode during the procedure for pairing, after the pairing has been carried out, the tag switching to non-connectable mode in order to prevent a new connection and therefore a new pairing.