Sterile connection system between an internal sterile chamber of a vial for containing medical or nutritional active substances and a tube for drawing said active substances and mixing them with a liquid diluent solution maintained in sterile conditions in a container, wherein: • the vial has a head provided with a hermetic closing plug in pierceable plastic material on which an outer pierceable sealing film or membrane is placed which is capable of maintaining the plug in sterile conditions; • the drawing and mixing tube has a hollow piercing tip which extends coaxially inside a terminal for attachment to the head of the vial and is provided with a protection cap able to keep said piercing tip in sterile conditions; • said protection cap is in axially compressible material with such a compression resistance to allow the cap to pierce said outer sealing film or membrane of the plug of the vial in a first advancement step of the terminal of the drawing and mixing tube to the head of the vial; characterized in that • said closing plug is in a plastic material having a higher rigidity than said compressible cap and has an internal sterile chamber located between said outer sealing film or membrane and an inner pierceable membrane arranged to close hermetically the internal chamber of the vial; • said internal sterile chamber of the closing plug includes a seat for abutment of the end of said compressible cap in a second step of advancement of the terminal of the drawing and mixing tube to the head of the vial after piercing of the outer sealing film or membrane of the plug and a passage of communication with said inner pierceable membrane to allow, in a final step of hooking of the terminal of the tube to the head of the vial, the axial compression of said compressible cap and the further advancement of said piercing tip to pierce the end of said compressible cap and then said inner pierceable membrane of the plug of the vial to put in sterile communication the internal chamber of the vial and said drawing and mixing tube. • the vial has a head provided with a hermetic closing plug in pierceable plastic material on which an outer pierceable sealing film or membrane is placed which is capable of maintaining the plug in sterile conditions; • the drawing and mixing tube has a hollow piercing tip which extends coaxially inside a terminal for attachment to the head of the vial and is provided with a protection cap able to keep said piercing tip in sterile conditions; • said protection cap is in axially compressible material with such a compression resistance to allow the cap to pierce said outer sealing film or membrane of the plug of the vial in a first advancement step of the terminal of the drawing and mixing tube to the head of the vial; characterized in that • said closing plug is in a plastic material having a higher rigidity than said compressible cap and has an internal sterile chamber located between said outer sealing film or membrane and an inner pierceable membrane arranged to close hermetically the internal chamber of the vial; • said internal sterile chamber of the closing plug includes a seat for abutment of the end of said compressible cap in a second step of advancement of the terminal of the drawing and mixing tube to the head of the vial after piercing of the outer sealing film or membrane of the plug and a passage of communication with said inner pierceable membrane to allow, in a final step of hooking of the terminal of the tube to the head of the vial, the axial compression of said compressible cap and the further advancement of said piercing tip to pierce the end of said compressible cap and then said inner pierceable membrane of the plug of the vial to put in sterile communication the internal chamber of the vial and said drawing and mixing tube.