The description relates to a filler container for filling a writing, painting or drawing device, a cosmetic application device or the like, where the device (44) has a capillary-action applicator (48) for a relatively low-viscosity fluid projecting from a housing, a reservoir for the fluid in fluid connection with the applicator (48) and an air-bleed channel (78) near the applicator (48). The filler container (10) has a neck section (58). The device (44) to be filled can be inserted with its applicator (48) and a housing section (46) continuing from the applicator (48) in the neck section (58) of the filler container in such a way that the neck section is sealed by said housing section (46) and a fluid connection is established by the air bleed channel (78) between the filler container (10) and the reservoir in the device (44).