Remdesivir is a drug initially developed for treating Hepatitis C but later proposed for numerous other diseases, such as Covid-19. However, the discovery of efficacy for new therapeutic indications of an existing drug indicates the practice of follow-on drugs, which is the development of secondary versions of an existing drug. In this context, granting new patents delays the entry of generic medicines onto the market, a ploy that the literature calls evergreening. Thus, using an empirical-qualitative study and documentary analysis, this article aimed to analyze patent applications related to Remdesivir at the INPI. It sought to answer the following research question: what elements relating to the structure of evergreening can be extracted from the Remdesivir case study? The first step in answering the question was to conceptualize follow-on drugs and evergreening. Subsequently, data on Remdesivir was collected from the Orange Book, Patentscope, Google Patents, and INPI platforms. The qualitative analysis of the data, based on the existence of a constant tension between the private monopoly and the public interest, according to May and Sell (2006), led to the conclusion that the pharmaceutical company Gilead Sciences Inc. holds four patents for therapeutically equivalent versions of Remdesivir in Brazil. In conclusion, it was possible to observe that the patenting of follow-on drugs is a form of evergreening since, in the specific case of Remdesivir, it caused the extension of the laboratory's patent monopoly by seven years, four months, and 25 days.