Method for predicting that a rotary drive member to be monitored should pass a critical threshold relating to structural condition - such as a defect of the rotary drive member to be monitored - after a certain rotation - duration of rotation or number of revolutions, the rotary drive member to be monitored forming part of a drive train comprising several mutually co-operating drive members (3a, 3b) of an apparatus, machine or mechanical assembly, such as a wheel, an axle co-operating with the wheel, a bearing unit having rolling bodies co-operating with the axle and with a chassis, and, if necessary, a device for driving the axle in rotation of which one rotary drive member is to be used for measuring purposes, wherein: ▪ a parameter indicative of the rotation conditions of the rotary drive member to be measured characteristic of the structural condition of the rotary drive member to be monitored is defined, ▪ a law of evolution of the indicative parameter as a function of the rotation of the rotary drive member to be monitored - cumulative number of revolutions or duration of rotation - taking account of the nature of said structural condition in question is available or is calculated on the basis of historical indicative parameters, ▪ at least one value of said indicative parameter - or function of said indicative parameter - is defined which is characteristic of said significant threshold corresponding to said given structural condition, threshold of the number of revolutions or duration of rotation, ▪ during a measuring or calculating operation when the drive train is rotating, the indicative parameter on the rotary drive member used for measuring purposes is measured or the indicative parameter is calculated on the basis of at least one rolling parameter measured on the rotary drive member used for measuring purposes, ▪ the measured or calculated value of the indicative parameter is correlated with the corresponding cumulative number of revolutions or duration of rotation of the rotary drive member to be monitored, ▪ during a comparison operation, on the basis of the measured or calculated value of the indicative parameter and the law of evolution, said corresponding cumulative number of revolutions or duration of rotation of the rotary drive member to be monitored is compared with the threshold of the number of revolutions or duration of rotation, and the number of revolutions or duration of rotation needed in order to reach the threshold of the number of revolutions or duration of rotation is deduced. ▪ a parameter indicative of the rotation conditions of the rotary drive member to be measured characteristic of the structural condition of the rotary drive member to be monitored is defined, ▪ a law of evolution of the indicative parameter as a function of the rotation of the rotary drive member to be monitored - cumulative number of revolutions or duration of rotation - taking account of the nature of said structural condition in question is available or is calculated on the basis of historical indicative parameters, ▪ at least one value of said indicative parameter - or function of said indicative parameter - is defined which is characteristic of said significant threshold corresponding to said given structural condition, threshold of the number of revolutions or duration of rotation, ▪ during a measuring or calculating operation when the drive train is rotating, the indicative parameter on the rotary drive member used for measuring purposes is measured or the indicative parameter is calculated on the basis of at least one rolling parameter measured on the rotary drive member used for measuring purposes, ▪ the measured or calculated value of the indicative parameter is correlated with the corresponding cumulative number of revolutions or duration of rotation of the rotary drive member to be monitored, ▪ during a comparison operation, on the basis of the measured or calculated value of the indicative parameter and the law of evolution, said corresponding cumulative number of revolutions or duration of rotation of the rotary drive member to be monitored is compared with the threshold of the number of revolutions or duration of rotation, and the number of revolutions or duration of rotation needed in order to reach the threshold of the number of revolutions or duration of rotation is deduced.