A tire which, during use is subjected to one or more severe stresses lead to an appreciable reduction of its potential lifetime of use under nominal conditions. In order to be able to determine whether a tire has undergone such severe conditions, the tire is provided with a monitoring device, containing at least one means sensitive to a given stress and capable of memorizing a piece of information, according to the stress to which the component has been subjected for at least a given time or a given number of cycles.