a body (10) a reservoir (20) a dispenser head (100) incorporating a dispenser orifice (5) and a dispenser member (30) , such as a pump or a valve, that is mounted on said reservoir (20) , said dispenser member (30) comprising a dispenser-member body (31) and a movable member (35) that moves axially in said dispenser-member body while said dispenser member (30) is being actuated said device further comprises a lateral actuator system (40) that is secured to said body (10), said lateral actuator system comprising at least one actuator element (41) that co-operates with said reservoir (20) , with said dispenser member (30) , or with an element that is secured to said reservoir (20) and/or to said dispenser member (30), said at least one actuator element (41) being movable between a rest position in which said dispenser member (30) is not actuated, and an actuated position in which said dispenser member (30) is actuated, said body (10) including at least one guide surface (50) for guiding said at least one actuator element (41), said guide surface (50) being stationary relative to said dispenser head (100), and substantially parallel to the movement axis of the movable member (35) in the dispenser-member body (31) while said dispenser member (30) is being actuated.