The policy debate around researchers' geographic mobility has been moving away from a theorized zero-sum game in which countries can be winners (brain gain) or losers (brain drain), and toward the concept of brain circulation, which implies that researchers move in and out of countries and everyone benefits. Quantifying trends in researchers' movements is key to understanding the drivers of the mobility of talent, as well as the implications of these patterns for the global system of science, and for the competitive advantages of individual countries. Existing studies have investigated bilateral flows of researchers. However, in order to understand migration systems, determining the extent to which researchers have worked in more than two countries is essential. This study focuses on the subgroup of highly mobile researchers whom we refer to as peripatetic researchers or super-movers. More specifically, our aim is to track the international movements of researchers who have published in more than two countries through changes in the main affiliation addresses of researchers in over 62 million publications indexed in the Web of Science database over the 1956-2016 period. Using this approach, we have established a longitudinal dataset on the international movements of highly mobile researchers across all subject categories, and in all disciplines of scholarship. This article contributes to the literature by offering for the first time a snapshot of the key features of highly mobile researchers, including their patterns of migration and return migration by academic age, the relative frequency of their disciplines, and the relative frequency of their countries of origin and destination. Among other findings, the results point to the emergence of a global system that includes the USA and China as two large hubs, and England and Germany as two smaller hubs for highly mobile researchers.