This paper contributes to the econometric literature on structural breaks by proposing a test for parameter stability in VAR models at a particular frequency w, where w [0, p]. When a dynamic model is affected by a structural break, the new tests allow for detecting which frequencies of the data are responsible for parameter instability. If the model is locally stable at the frequencies of interest, the whole sample size can be then exploited despite the presence of a break. Two empirical examples illustrate that local stability can concern only the lower frequencies (change in the U.S. monetary policy in the early 80'(s) or higher frequencies (decrease in the postwar U.S. productivity).