A fluid dispenser device comprising: a fluid dispenser orifice (31); an air duct (32, 51, 52) for air under pressure, said air duct including an upstream end and a downstream end that opens out in the proximity of the orifice (31); an air expeller (4) that is suitable for being subjected to elastic squeezing and relaxation stages, the air expeller (4) being connected to the air duct (32, 51, 52) so that, during elastic squeezing stages, it delivers a flow of air through the air duct until it reaches the orifice (31); and a fluid channel (25, 33) that is connected to the air duct (32, 51, 52), the fluid in the channel (25, 33) being sucked up by the flow of air under pressure by the Venturi effect; the device being characterized in that the air expeller (4) has only a single opening (43) that is provided with a connection sleeve (5) that includes an incoming-air passage (53) that is provided with an air-inlet valve (56; 56b; 56c; 56d) that is suitable for allowing outside air to enter into the air expeller during elastic relaxation stages.