INTRODUCTION. Research software plays an increasingly vital role in the scholarly record. Academic research libraries are in the early stages of exploring strategies for curating and preserving research software, aiming to provide long-term access and use. DESCRIPTION OF PROGRAM. In 2016, the Council on Library and Information Resources (CLIR) began offering postdoctoral fellowships in software curation. Four institutions hosted the initial cohort of software curation fellows. This article describes the work activities and research program of the cohort, highlighting the challenges and benefits of doing this exploratory work in research libraries. NEXT STEPS. Academic research libraries are poised to play an important role in research and development around robust services for software curation. The next cohort of CLIR fellows are set to begin in fall 2018 and will likely shape and contribute substantially to an emergent research agenda.