A recent study in the USA documented the existence and growth of "excellence gaps" among students. These gaps are similar to the minimum competency achievement gaps that proliferate in policy discussions in many Western countries, but excellence gaps focus on the highest level of achievement rather than minimum competency. We extend this research using an international approach, data from the most recent Trends in International Mathematics and Science Study, and a multilevel model for change to examine excellence gap trends with specific emphasis on sex and immigrant status of the student. At an international level, sex-based findings are encouraging. Specifically, we found evidence of shrinking sex-based excellence gaps in both science and mathematics. With respect to immigrant status and excellence gaps, small gaps in the proportion of advanced achievers persist over time. In the context of large demographic changes worldwide, we argue that these findings are generally encouraging. (Contains 6 tables, 12 figures, and 2 notes.)