Basic system for diagnosing the structural state of at least one rotary kinematic member which is to be diagnosed of a kinematic chain of an apparatus, a machine, or a device, in particular a wheeled for movement thereof on a network of tracks, said kinematic chain having a plurality of rotary kinematic members which are associated with one another, including a measuring and collecting rotary kinematic member, at least one rolling bearing unit, the plurality of rotary kinematic members being in particular at least one wheel, at least one axle which is associated with the wheel, the at least one rolling bearing unit being associated with the axle and the chassis of the device, and, where appropriate, at least one device for rotating the axle, which system comprises: an apparatus for measuring and collecting the value of at least one parameter of the rolling conditions of the rotary kinematic member, this parameter being characteristic of the structural state of the rotary kinematic member to be diagnosed, this measuring and collecting apparatus being on board the apparatus, the machine, or the device, structurally and functionally associated with the measuring and collecting rotary kinematic member and capable of measuring and collecting the values of said parameter and of providing data characteristic of the rolling conditions of the rotary kinematic member to be diagnosed, where appropriate, by means of functionally associated processing means, a data storage means which is on board the apparatus, the machine, or the device, a calculation and analysis means which is capable, on the basis of variations in said characteristic data, in a frequency corresponding to the rotary kinematic member to be diagnosed and in at least one predetermined significant value of, or function of, the characteristic parameter, of providing diagnostic information regarding the present or predicted structural state of the rotary kinematic member to be diagnosed, characterized in that the rotary kinematic member to be diagnosed is different from the measuring and collecting rotary kinematic member. an apparatus for measuring and collecting the value of at least one parameter of the rolling conditions of the rotary kinematic member, this parameter being characteristic of the structural state of the rotary kinematic member to be diagnosed, this measuring and collecting apparatus being on board the apparatus, the machine, or the device, structurally and functionally associated with the measuring and collecting rotary kinematic member and capable of measuring and collecting the values of said parameter and of providing data characteristic of the rolling conditions of the rotary kinematic member to be diagnosed, where appropriate, by means of functionally associated processing means, a data storage means which is on board the apparatus, the machine, or the device, a calculation and analysis means which is capable, on the basis of variations in said characteristic data, in a frequency corresponding to the rotary kinematic member to be diagnosed and in at least one predetermined significant value of, or function of, the characteristic parameter, of providing diagnostic information regarding the present or predicted structural state of the rotary kinematic member to be diagnosed, characterized in that the rotary kinematic member to be diagnosed is different from the measuring and collecting rotary kinematic member.