Abstract: A container closure construction comprises a container which has an externally threaded neck portion, with a top opening and with a rim encircling the opening and with a cap bead receiving recess defined below the rim around the exterior of the neck portion. The closure includes an inner closure cap having a cap part which overlies the container opening and an annular side skirt portion which is engaged around the exterior of the container neck portion, and which includes an inwardly extending cap bead engaged in a cap receiving recess of the container. A hollow central part extends through this cap part which goes above the exterior face and below the interior face and it defines an opening therethrough. An outer cover has an internally threaded outer cover skirt part which threadably engages with the externally threaded neck portion of the container.