A medical product is configured for use in a medical system. A method is provided for sterilizing the product. A connector connects a first subsystem and a second subsystem, containing a medical fluid, for transport of the medical fluid from the second subsystem to the first subsystem. The connector comprises a valve device, a first connection pipe connected to the first subsystem, and a second connection pipe connected to the second subsystem. The valve device comprises a first part and a second part movable relative to each other to permit an opening movement from a closed stable position, which prevents a fluid communication between the connection pipes, to an open position, which establishes a channel permitting the fluid communication. The connector comprises at least one small passage permitting, in the closed stable position, an introduction of a sterilizing gas to contact wall surfaces defining the channel.