The invention concerns a method of collecting a biological fluid, in particular blood, with an anticoagulant and/or preservation solution added, in which the biological fluid is collected by natural flow and the anticoagulant and/or preservation solution is added by pumping, the method making provision for measuring the flow of fluid collected and slaving the pumping speed to the measured flow, so as to obtain continuously during collection a given ratio between the quantity of fluid collected and the quantity of anticoagulant and/or preservation solution added. The invention also concerns a collection machine and bag system for implementing the method.