It is well known that a crucial property for the effective identification of time-varying systems is that the data carry continual information on the parameters to be estimated. As a matter of fact, only in this case can the identification algorithm rely on fresh information in forming a reliable estimate of the current value of these parameters. This concept has been formalized in the system identification literature under the name of persistence of excitation. In this paper, the persistence of excitation property is studied for a class of time-varying systems (that includes the standard autoregressive model as a particular case) and conditions for it to hold are derived.