Abstract: The disclosed method enables a network of message senders to send imposed messages to mobile electronic devices connected to one or more cell telecommunications networks, discreetly, in a way that is not cumbersome for the user of the targeted device, and costs little in terms of occupancy of the communications network being exploited. Furthermore, the message senders' network sends its messages through a cell telephony network, and more particularly through the data channels of this network. The imposed message is stored in a specific memory of the electronic device considered. It can thus be restituted several times to the output units of the electronic device in having been transmitted only once in the device. Means are proposed to manage the restitution of the imposed message thus stored.