A double packaging structure for an object, which may be a sterile object, includes a hollow external container having a closed first end, an open second end and walls, and an internal container disposed inside the external container. The internal container includes a hollow body and a cap. The object is intended to be received in the body. To close its first end, the external container has a membrane capable of deforming when pressure is applied to the membrane. The membrane is configured so that a pressure applied to its outer face, along the longitudinal axis, pushes its inner face against the inner container and causes the inner container to exit at the second end of the external container in the absence of a closure system at the second end.