Applicator device comprising: - a reservoir suitable for containing a product to be applied, this reservoir extending along a central axis between a proximal end and a distal end, and said reservoir being axially open at said distal end, - a cap that is connected to the distal end of the reservoir, said cap comprising an opening on the central axis, - a spherical plug valve mounted in the cap so as to pivot about a transverse axis perpendicular to the central axis, said plug valve comprising a central passage perpendicular to the transverse axis and said plug valve pivotable between: * a closed position in which said plug valve closes the opening in the cap, * and an open position in which said central passage of the plug valve is aligned with the opening in the cap, - a plug valve control member, movable between a closed position and an open position, and able to place the plug valve in the closed position when said plug valve control member is in the closed position and to place the plug valve in the open position when said plug valve control member is in the open position, - a rod extending along the central axis to a free end equipped with an applicator head suitable for applying said product, said rod being movable at least translationally along the central axis, between: * a retracted position in which the applicator head is positioned within the reservoir, * and an extended position in which the rod traverses the central passage of the plug valve and the applicator head is outside the reservoir, wherein the plug valve control member is rotatable about the central axis, between the closed position and the open position, wherein the reservoir is mounted within an external body solidly connected to the cap, and wherein the rod traverses the proximal end of the reservoir and is mounted in a base which axially extends the reservoir from the proximal end of said reservoir, said base being movable relative to the external body along an actuating path comprising a first path section between a rest position and an intermediate position, and a second path section between said intermediate position and a utilization position, said first path section comprising a rotational movement of the base relative to the external body about the central axis, said base being coupled to the plug valve control member so as to rotate said plug valve control member from the closed position to the open position when the base is moved from the rest position to the intermediate position, and said base being adapted to move the rod from the retracted position to the extended position during the second path section. - a reservoir suitable for containing a product to be applied, this reservoir extending along a central axis between a proximal end and a distal end, and said reservoir being axially open at said distal end, - a cap that is connected to the distal end of the reservoir, said cap comprising an opening on the central axis, - a spherical plug valve mounted in the cap so as to pivot about a transverse axis perpendicular to the central axis, said plug valve comprising a central passage perpendicular to the transverse axis and said plug valve pivotable between: * a closed position in which said plug valve closes the opening in the cap, * and an open position in which said central passage of the plug valve is aligned with the opening in the cap, * a closed position in which said plug valve closes the opening in the cap, * and an open position in which said central passage of the plug valve is aligned with the opening in the cap, - a plug valve control member, movable between a closed position and an open position, and able to place the plug valve in the closed position when said plug valve control member is in the closed position and to place the plug valve in the open position when said plug valve control member is in the open position, - a rod extending along the central axis to a free end equipped with an applicator head suitable for applying said product, said rod being movable at least translationally along the central axis, between: * a retracted position in which the applicator head is positioned within the reservoir, * and an extended position in which the rod traverses the central passage of the plug valve and the applicator head is outside the reservoir, * a retracted position in which the applicator head is positioned within the reservoir, * and an extended position in which the rod traverses the central passage of the plug valve and the applicator head is outside the reservoir,