A fluid dispenser device has a container filled with two concentric squeezeable tubes that has two concentric threaded outlets. The two threaded outlets are secured to an internal cap that has fluid passages for both outlets and external threaded sections for engaging the inner shell and an outer shell. The internal cap also has two barrier members on its outer walls that engage with the inner shell's sliders that releasably engage the inner shell in its open or closed positions. The inner shell threadingly engages a conduit unit that when lowered closes the fluid passages with projecting stubs and when raised opens those passages to allow dispensation from the container. The external cap has internal splines that engages the internal cap's external grooves. When the external cap is removed, the internal cap is rotated which in turn rotates and raises the conduit unit which opens the valves. When the external cap is secured and rotated onto the internal cap's threads, the inner shell rotates which in turn lowers the conduit unit to close the valves.