Method for transferring unwinders for supplying elastomeric products to green tyre manufacturing machines using a transfer facility, each product being wound on a reel, the said facility comprising a control unit, unwinders, and at least one autonomous mobile platform able to support and to move a unwinder, each unwinder being able to support a reel and to collaborate with the green tyre manufacturing machine in such a way as to unwind the product wound on said reel and supply said machine with product, the method being characterized in that said facility comprises evaluation means for evaluating the state of the unwinders, said evaluation means comprising measurement means for measuring the quantity of product wound on reels supported by the said unwinders, and communication means able to transmit the data measured by said measurement means to the control unit, the method comprising the following successive operations: measuring the quantity of product wound on the reels supported by the said unwinders supplying the green tyre manufacturing machines, using the measurement means, and communicating the measured data to the control unit using the communication means, on the basis of the measured data, determining, using the control unit, the moment at which to transmit a removal or supply mission instruction to a mobile platform so that the mobile platform becomes positioned underneath the unwinder that is intended to be removed from a green tyre manufacturing machine before or at the moment at which the unwinder is to be removed, and/or in such a way that the unwinder intended to supply a green tyre manufacturing machine becomes positioned in the immediate vicinity of the said green tyre manufacturing machine by means of a mobile platform before or at the moment at which the unwinder is to be transferred into the green tyre manufacturing machine, transmitting to a mobile platform at the previously-determined moment, mission instructions to remove or to supply a unwinder, moving the mobile platform in such a way that it becomes positioned underneath the unwinder that is intended to be removed from a green tyre manufacturing machine, or moving the mobile platform supporting the unwinder intended to supply a green tyre manufacturing machine so that it becomes positioned in the immediate vicinity of the green tyre manufacturing machine. measuring the quantity of product wound on the reels supported by the said unwinders supplying the green tyre manufacturing machines, using the measurement means, and communicating the measured data to the control unit using the communication means, on the basis of the measured data, determining, using the control unit, the moment at which to transmit a removal or supply mission instruction to a mobile platform so that the mobile platform becomes positioned underneath the unwinder that is intended to be removed from a green tyre manufacturing machine before or at the moment at which the unwinder is to be removed, and/or in such a way that the unwinder intended to supply a green tyre manufacturing machine becomes positioned in the immediate vicinity of the said green tyre manufacturing machine by means of a mobile platform before or at the moment at which the unwinder is to be transferred into the green tyre manufacturing machine, transmitting to a mobile platform at the previously-determined moment, mission instructions to remove or to supply a unwinder, moving the mobile platform in such a way that it becomes positioned underneath the unwinder that is intended to be removed from a green tyre manufacturing machine, or moving the mobile platform supporting the unwinder intended to supply a green tyre manufacturing machine so that it becomes positioned in the immediate vicinity of the green tyre manufacturing machine.