A anti-drip cap for a deformable vial, in particular a flexible vial, containing a cosmetic, pharmaceutical, industrial or food product in liquid or creamy form, comprising: - a substantially tubular base which is intended to be hermetically attached to a tubular neck complementary to the vial, and a first tubular section of which comprises at least one lower inlet port communicating with the neck of the vial, - a substantially tubular lid which hermetically covers the base, and a second tubular section of which is closed by at least one "upper" transverse wall comprising at least one so-called upper outlet port for the product, the first and second tubular sections (22, 23) being slidably mounted into each other and hermetically determining a product flow chamber interposed between the inlet port of the base and the product outlet port, one end of one of the tubular sections, so-called internal tubular section, which is slidably mounted within the other section, so-called outer section, being arranged within the flow chamber, said lid being vertically movable between at least: - a low closure and locking position, in which the lid is blocked on the base and in which the product outlet port is lowered on a closure element which protrudes, coaxially to the base, from its upper transverse wall, said closure element closing the product outlet port, - a middle position, in which the relative positions of the lid and the base determine a discharge path with reduced dimensions making the product outlet port communicate with the flow chamber to obtain venting of the flexible vial allowing, in particular, the flexible vial to recover its shape when pressed, - an upper dispensing position, in which the outlet port is arranged with a large clearance determined above the closure element to allow the product to pass through the inlet and outlet ports and the flow chamber, once the flexible vial is pressed, characterized in that the end of the inner tubular section arranged within the flow chamber has at least one substantially truncated cone-shaped lip which laps an inner bore of the outer tubular section, and in that the coaxial closure element has a fourth cylindrical lower section, a fifth substantially truncated cone-shaped middle section, the diameters of which are lower than that of the fourth section, and a sixth truncated cone-shaped upper section complementary to the port of the lid, and in that the lid has a seventh tubular section which coaxially extends into the second tubular section from the upper transverse wall, with a diameter corresponding to that of the fourth section of the closure element, and the free end of which, arranged at the junction of the fourth and fifth sections (70, 72) in the middle position of the lid to obtain venting of the vial, has a second truncated cone-shaped lip intended to lap the fourth lower section of the coaxial closure element. - a substantially tubular base which is intended to be hermetically attached to a tubular neck complementary to the vial, and a first tubular section of which comprises at least one lower inlet port communicating with the neck of the vial, - a substantially tubular lid which hermetically covers the base, and a second tubular section of which is closed by at least one "upper" transverse wall comprising at least one so-called upper outlet port for the product, the first and second tubular sections (22, 23) being slidably mounted into each other and hermetically determining a product flow chamber interposed between the inlet port of the base and the product outlet port, one end of one of the tubular sections, so-called internal tubular section, which is slidably mounted within the other section, so-called outer section, being arranged within the flow chamber, said lid being vertically movable between at least: - a low closure and locking position, in which the lid is blocked on the base and in which the product outlet port is lowered on a closure element which protrudes, coaxially to the base, from its upper transverse wall, said closure element closing the product outlet port, - a middle position, in which the relative positions of the lid and the base determine a discharge path with reduced dimensions making the product outlet port communicate with the flow chamber to obtain venting of the flexible vial allowing, in particular, the flexible vial to recover its shape when pressed, - an upper dispensing position, in which the outlet port is arranged with a large clearance determined above the closure element to allow the product to pass through the inlet and outlet ports and the flow chamber, once the flexible vial is pressed, - a low closure and locking position, in which the lid is blocked on the base and in which the product outlet port is lowered on a closure element which protrudes, coaxially to the base, from its upper transverse wall, said closure element closing the product outlet port, - a middle position, in which the relative positions of the lid and the base determine a discharge path with reduced dimensions making the product outlet port communicate with the flow chamber to obtain venting of the flexible vial allowing, in particular, the flexible vial to recover its shape when pressed, - an upper dispensing position, in which the outlet port is arranged with a large clearance determined above the closure element to allow the product to pass through the inlet and outlet ports and the flow chamber, once the flexible vial is pressed,