A two-channel dispensing device intended to close a vial includes two reservoirs (13, 14), two channels having an inlet end opening into one of the reservoirs and outlet end opening outside of the reservoir. First closing means are provided in each channel, which can change from a closed position to an opened position in which a product can exit said reservoir. The two channels are isolated from each other at least between their inlet ends and the respective closing means. The reservoirs are formed by a single flexible pouch separated by a central partition (12) into first and second compartments (13, 14) performing the functions of the first and second reservoirs. The inlet end of the first channel opens into the first compartment (13) and the inlet end of the second channel opens into the second compartment (14), so that a single pouch makes it possible to form two reservoirs.