In a nipple for a baby feeding container, a valve part is disclosed, comprising a unidirectional valve formed of a pliable material and oppositely oriented such that when attached to the container a normal fluid flow through the valve is into the container while a flow from the container to the outside is normally blocked, the valve is characterized by a plurality of normally closed non intersecting slits formed in a deformable wall which blocks the flow of liquid from the container to the outside unless when the slits become temporarily distorted by the natural mouth maneuverings of a baby. The valve is especially advantageous for use in baby feeding containers of inflatable type in which the liquid content is pressurized under the pressure exerted by the stretched elastomeric walls of the container.