System for diagnosing the structural condition of a plurality of rolling units, each having a unique identifying datum, mounted on a machine having wheels in order to move it on a network of tracks, in particular a train, comprising: ▪ apparatuses for measuring and collecting, over time, the value of at least one parameter pertaining to the rolling conditions of the rolling units characteristic of their structural condition, structurally and functionally associated with the plurality of rolling units, installed on board the machine, configured to measure and collect the values of said parameter and supply data characteristic of the rolling conditions of each of the rolling units, if necessary with the aid of functionally associated processing means, ▪ data storage means installed on board the machine, configured to store said characteristic data supplied by the measuring and collecting apparatuses and the identification data of the rolling units, ▪ means for communicating data via a wireless link, installed on board the machine, ▪ at least one data collection unit, structurally dissociated from the machine, ▪ calculation and analysis means, characterised in that: ▪ the means for communicating data via a wireless link within a certain coverage area are functionally associated with the data storage means and configured to transfer said characteristic data and the stored identification data, ▪ the at least one data collection unit is configured to be structurally positioned relative to a track in the coverage area of the communication means installed on board the machine located on this track and thus collect said characteristic data and the stored identification data, ▪ the calculation and analysis means are structurally dissociated from the machine, configured to be functionally associated with the collection unit and configured, on the basis of said characteristic data and at least one predetermined significant value of - or as a function of - the characteristic parameter, to supply diagnostic information pertaining to the current or projected structural condition of each of the rolling units. ▪ apparatuses for measuring and collecting, over time, the value of at least one parameter pertaining to the rolling conditions of the rolling units characteristic of their structural condition, structurally and functionally associated with the plurality of rolling units, installed on board the machine, configured to measure and collect the values of said parameter and supply data characteristic of the rolling conditions of each of the rolling units, if necessary with the aid of functionally associated processing means, ▪ data storage means installed on board the machine, configured to store said characteristic data supplied by the measuring and collecting apparatuses and the identification data of the rolling units, ▪ means for communicating data via a wireless link, installed on board the machine, ▪ at least one data collection unit, structurally dissociated from the machine, ▪ calculation and analysis means, ▪ the means for communicating data via a wireless link within a certain coverage area are functionally associated with the data storage means and configured to transfer said characteristic data and the stored identification data, ▪ the at least one data collection unit is configured to be structurally positioned relative to a track in the coverage area of the communication means installed on board the machine located on this track and thus collect said characteristic data and the stored identification data, ▪ the calculation and analysis means are structurally dissociated from the machine, configured to be functionally associated with the collection unit and configured, on the basis of said characteristic data and at least one predetermined significant value of - or as a function of - the characteristic parameter, to supply diagnostic information pertaining to the current or projected structural condition of each of the rolling units.