An anti-theft device for containers of fluid products comprising: a support element (3) connected to a container (2) to be monitored and attached to the inside of a neck (6) of container (2), between the neck (6) itself and a closure member (11) which is irremovably attached to container (2); and a circuit (7) at least partially housed in said support element (3) to receive an enquiry signal (S1) and to generate a corresponding response signal (S2).