A safety device for a cylinder holding gaseous fluids under pressure is disclosed. The safety device has a device body in which a passage is defined for a fluid; the passage extends from an entry aperture, suitable for being placed in fluidic communication with a cylinder, to an exit aperture. An obturator air tightly engages the passage, the obturator is movable from a first position, in which it indicates the presence of fluid at a pressure below a first predefined pressure threshold value, inside the cylinder, and a second position, in which it indicates the presence of fluid at a pressure above the first predefined pressure threshold value inside the cylinder. At least one temperature and/or pressure-sensitive relief device is positioned in the obturator in such a way that, upon exceeding a predefined temperature threshold or upon exceeding a second predefined pressure threshold, the relief device opens the passage for the fluid and permits the flow of fluid from the entry aperture towards the exit aperture.