Evolution can occur both gradually and through alternating episodes of stasis and rapid changes. However, the prevalence and magnitude of fluctuations of the rate of evolution remains obscure. Detecting a rapid burst of changes requires a detailed record of past evolution, so that events that occurred within a short time interval can be identified. Here, we use the phylogenies of the Baikal Lake amphipods and of Catarrhini, which contain very short internal edges facilitating this task. We detect 6 radical bursts of evolution of individual proteins during such short time periods, each involving between 6 and 38 amino acid substitutions. These bursts were extremely unlikely to have occurred neutrally, and were apparently caused by positive selection. On average, in the course of a time interval required for one synonymous substitution per site, a protein undergoes a strong burst of rapid evolution with probability at least ~0.01.