A connection system connects a plasma torch to a generator to allow the passage of electric current, the passage of an operating fluid, and of one or more control signals between the generator and the torch. The system includes a first connector and a second connector that are removably connected to each other. The first connector includes a first current-carrying terminal and the second connector having a second current-carrying terminal. The current-carrying terminals are suited to be mutually connected to each other. The first connector includes one or more electric terminals. The second connector includes one or more electric terminals, the connectors being suited to be mutually connected to each other. In the first connector, the electric terminals are movable with respect to the first terminal.