The present study focuses on persistence in research productivity over the course of an individual’s entire scientific career. We track “late-career” scientists—scientists with at least 25 years of publishing experience (N = 320,564)—in 16 STEMM (science, technology, engineering, mathematics, and medicine) and social science disciplines from 38 OECD countries for up to 5 decades. Our OECD sample includes 79.42% of late-career scientists globally. We examine the details of their mobility patterns as early-career, midcareer, and late-career scientists between decile-based productivity classes, from the bottom 10% to the top 10% of the productivity distribution. Methodologically, we turn a large-scale bibliometric data set (Scopus raw data) into a comprehensive, longitudinal data source for research on careers in science. The global science system is highly immobile: Half of global top performers continue their careers as top performers and one-third of global bottom performers as bottom performers. Jumpers-Up and Droppers-Down are extremely rare in science. The chances of moving radically up or down in productivity classes are marginal (1% or less). Our regression analyses show that productivity classes are highly path-dependent: There is a single most important predictor of being a top performer, which is being a top performer at an earlier career stage.