The invention is a fluid dispensing device suited to be connected, by means of a connection element (220), to a container (C) holding the fluid that can be dispensed from the inside to the outside of the container through an actuator element (400), comprising: a suction duct (240) suited to communicate with the fluid held inside the container (C), a dispenser duct (440) in communication with the outer space with respect to the volume (V) enclosed by the container (C), a suction/compression chamber (300) that can communicate with the suction duct (240) and the dispenser duct (440), a suction valve (260) suited to alternatively allow and prevent the passage of a fluid between the suction duct (240) and the suction/compression chamber (300) when, respectively, the suction valve is closed and open, a dispensing valve (460) suited to alternatively allow and prevent the passage of a fluid between the dispenser duct (440) and the suction/compression chamber (300) when, respectively, the suction valve is closed and open, a tight membrane (500) slidingly coupled with the walls of the suction/compression chamber (300) so that it can be translated in a predetermined direction; both the suction valve (260) and the dispensing valve (460) comprise the membrane (500). The invention concerns also a system for containing and dispensing fluids (F).