Data transmission method between an on-board device adapted to acquire data relating to motion and/or driving parameters of a vehicle and a remote processing center, comprising the steps of: acquiring said data through the on-board device and storing it in a log memory of the on-board device; assessing by means of the on-board device if a logical condition is satisfied; sending, if said logical condition is satisfied, by means of the on-board device, a data connection request message requesting connection to a mobile cellular radio network to request the establishment of a GPRS connection between the on-board device and the remote processing center; receiving the data connection request at the remote processing center, by means of the mobile cellular radio network; processing the data connection request message at the remote processing center to accept or reject the connection request based on said identifying data.