First and second sealed, sterile containers, having respectively communicating first and second fluid transfer tubes, the tubes having diaphragms occluding the bores thereof, may be connected together in sterile manner for the sterile transfer of the contents of one container to the other. To accomplish this, one point of a double-pointed, hollow spike is inserted into each of the bores of the fluid transfer tubes, at the free ends thereof, the spike being proportioned to tightly and sealingly fit into each bore of the fluid transfer tubes. Thereafter, the spike and that portion of the tubes extending from the diaphragms to the free ends thereof are sterilized. Then the points of the spike are moved to rupture the diaphragms, to open a flow channel, and the sterile contents are transferred. The fluid transfer tube of the container receiving the desired sterile contents is then resealed, prior to breaking sterility by opening the connection.